A returning net comes flying back into the hands of the creature that threw it, regardless of whether it hits or not. It’s easy to imagine the net flying back to its thrower when it misses. But once it has restrained its target, I can’t figure what happens. Does it bring back its taget?
It is up to the DM to decide
This is a case where we have a mechanic introduced from Unearthed Arcana that does not mesh clearly with the rules. It's unclear if WotC considered the net when coming up with this, but for whatever reason, that specific interaction isn't addressed – which means it's up to the DM to decide.
This is also a case where there isn't "one true" reading of the RAW. When there are multiple interpretations due to inconsistent wording or features that aren't accounted for, then it comes down to the DM to make a decision. Because the Returning Weapon simply doesn't account for the net interactions, there are multiple ways the RAW can be inferred.
So what to do?
Let's look at the class ability Returning Weapon first:
This magic weapon grants a +1 bonus to attack and damage rolls made with it, and it returns to the wielder’s hand immediately after it is used to make a ranged attack.
Now, you've got a net. You've thrown it. Whether it hits or misses, it returns.
That much we know.
But the net has other properties in that a successful hit causes the restrained condition and it dictates how that can be resolved.
A creature can use its action to make a DC 10 Strength check, freeing itself or another creature within its reach on a success. Dealing 5 slashing damage to the net (AC 10) also frees the creature without harming it, ending the effect and destroying the net.
At this point, you've got an issue that the specific rule around Returning Weapon doesn't provide any guidance for the case of the net. A DM needs to come up with a ruling at their table that works for everyone present at the table.
In these situations as DM, I generally come up with something I think is reasonable and talk to the table about it. As long as everyone agrees and is on-board with it, I think you've got a functional ruling. Whether or not you want to equate it with the other thrown weapon return mechanics is up to you.
How I'd rule
Really doesn't matter. Every table is different and how I'd rule really isn't applicable to any other table. Just talk it out and come up with something that works. But here are some considerations:
The net immediately returns and no longer restrains the target. This follows the class ability, but it clearly creates an issue for the net user. You could say that the Returning Weapon is more specific than the net rules, so it immediately returns. Which devalues the net immensely.
The net can stay until recalled. The problem here is that the net can be destroyed. This devalues the class ability, but it gives the thrower some control in when it returns and keeps the condition you're trying to impose.
The net returns, but the condition remains. This is a bit wonkier. Yeah, the net is magic, but the magic net never talks about working when it's not there. It just helps in attacking and dealing damage. This is interesting because the player would still get the net effects and the mechanic of Returning Weapon. You'd likely need to rule that the damage part of net removal remains (somehow), otherwise this gives more to the net's abilities then it normally has. That way, the net basically works the same as the other thrown options by doing what it does, and doing it without needing to have more than one net.
Net returns with target. This would vastly increase the power of the net. The ability doesn't state that other weapons currently embedded in the target would bring target back to the the artificer, either.
The rules simply don’t cover this case; it is entirely up to the DM to decide what happens.
Four possibilities spring to my mind:
The net returns, without the target, making the endeavor pointless.
The returning property fails entirely, the net being pinned in place by the target.
The target is dragged back to the artificer.
The returning is delayed until the target extricates itself from the net, at which point the net returns to the artificer.
None of these possibilities has any real rules support: returning does not mention that it frees any targets of a returning net, does not mention any situation in which the weapon can fail to return, certainly doesn’t mention any ability to bring a creature back with it, and doesn’t mention any opportunity for the returning to happen at any point later than immediately after the weapon hits or misses. Really, taken literally, the only thing the rules really do support is having the net return but the target remain restrained even so, as Amethyst Wizard’s fine answer explains. If that’s all the rules have to offer, I think it’s pretty clear that the DM needs to come up with something else.
For me, I think #4 is the most reasonable and balanced of these options. It seems most true to the purpose of the features, without causing any extra benefits—the returning property does its job and allows the artificer to retrieve their net at no extra effort on their part, but the net does its job restraining the target without giving the artificer any new or extra features not explicitly indicated by either returning or nets.
The net returns to the artificer and the target remains restrained until freed, RAW.
There are no special conditions indicated on the returning weapon. In common with other rulings, “it does what it says it does” applies in this case.
The weapon returns to the wielders hand immediately after it is used to make a ranged attack.
Returning Weapon: This magic weapon grants a +1 bonus to attack
and damage rolls made with it, and it returns to the wielder’s hand immediately after it is used to make a ranged attack UA Eberron Artificer.
The net is a special weapon, when it hits a target, that target is restrained until freed.
Net A large or smaller creature hit by a net is restrained until it is freed... A creature can use it's action to make a DC 10 Strength check, freeing itself or another creature within it's reach on a success. Dealing 5 slashing damage to the net also frees the creature without hurting it, ending the effect and destroying the net. PHB. 148
Lets put these together simply; An artificer makes a ranged attack with a net and hits, the creature hit by the net is restrained until it is freed, the net immediately returns to the artificer's hand.
The restrained creature remains in place, no forced movement is inferred from the net or artificer infusion rules.
There are only two ways to free a creature restrained by a net, either they are freed with a strength check, or slashing damage to the net frees the target.
Example of play: Crago the Artificer is setting up camp in the forest at twilight among his adventurer friends. From the nearby brush an angry boar charges toward Crago.
Crago acts quickly and throws his net over the boar (10 feet away). With the odds against him Crago still manages to restrain the boar with his net.
The net immediately returns to Crago's hands. The boar squeels as it attempts to free itself from restraint. Onlookers are bewildered as the boar is unable to free itself, Tondo exclaims "Crago, by what magic have you captured this boar?"
Crago replies "You think that was cool, watch this!" Crago walks 10 paces further away from the boar and takes out his dagger. Crago smirks then slashes the net he is holding, the net falls to the ground at Crago’s feet.
The boar grunts and scampers away into the night.
Tondo claps “Bravo! Bravo my friend.” 👏👏👏
By RAW, the net returns by itself to its wielder, though its unclear if the target is still restrained. However, the target is likely not restrained long enough to benefit the wielder.
net weapon states
Special. A Large or smaller creature hit by a net is restrained until it is freed. A net has no effect on creatures that are formless, or creatures that are Huge or larger. A creature can use its action to make a DC 10 Strength check, freeing itself or another creature within its reach on a success. Dealing 5 slashing damage to the net (AC 10) also frees the creature without harming it, ending the effect and destroying the net.
so, a creature is restrained until it is freed, as per the net description.
Returning Weapon states
This magic weapon grants a +1 bonus to attack and damage rolls made with it, and it returns to the wielder's hand immediately after it is used to make a ranged attack.
so, the weapon ('it') returns to the wielder after the attack is made. This means we need to refer to the Player's Handbook, chapter 9 (Combat), section - Making an Attack, specifically, Resolve the Attack
You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.
In this case, the net inflicts a condition instead of causing damage. Once the condition (Restrained) has been caused, the attack is complete, and the net can return to its wielder.
The question is, does the net returning to its wielder (leaving the target) count as 'freeing' the target?
The net lists two methods of freeing, a Strength check, or a slashing damage attack; but, it does use the word 'can' in reference to the check, indicating an option; and, it does not say these are the only methods, so we can consider other ones.
Because the net starts as non-magical, and Returning Weapon only grants the ability to return, no other magical properties, we can apply real world understanding.
Absent of magic, a net can only apply it properties while on a target. Because Returning Weapon removes the net from the target, it is no long on the target, which means the Restrained condition it causes can no longer apply.
This means that Returning Weapon would end the restrained condition, thus preventing preventing the only reason to use the net weapon in the first place.
UA Eberron Arificer states:
Returning Weapon: This magic weapon grants a +1 bonus to attack and damage rolls made with it, and it returns to the wielder’s hand immediately after it is used to make a ranged attack
So immediately after the net is used to make a ranged attack, it is returned to the owner's hands.
A Large or smaller creature hit by a net is restrained until it is freed. [...] A creature can use its action to make a DC 10 Strength check, freeing itself or another creature within its reach on a success. Dealing 5 slashing damage to the net (AC 10) also frees the creature without harming it, ending the effect and destroying the net.
Here we describe what the net does. It imposes restrained until the target is freed.
The rules text also lists two ways to become free; a DC 10 Strength check, or dealing 5 slashing damage to the net (which also destroys it).
Now, 5e D&D has no flavour text. So the first line still applies, and nothing here states those are the only 2 ways to become freed from a net.
Any other situation must, by the rules as written, be interpreted by the DM. The DM now has a choice.
The net is going to return. This return happens immediately after the attack.
The question the DM must answer is, "The net that was restraining the target is now 30' away in another creature's hands, and not touching the target. Is the target freed?"
What, exactly, the DM answers there is completely up to the DM, but the rules explicitly tell the DM to answer that question to determine if the creature is restrained or not; it places a condition on the restrained condition, and the DM is responsible to determine if it happens or not.
The DM could decide that a magic net (it is +1, after all) can restrain things without touching them or being anywhere near them. Or they could decide that being on the other side of a room from a net is one way of being "freed" from that net.
Now there is one ambiguity. When the net returns, nothing states what happens to the creature it is restraining. One possible interpretation is that the restrained creature is also moved to the thrower of the net, and ends up in the throwers hands.
I cannot find rules text to support either of these two options.
What does "returning" mean to you? The net flies back into the thrower's hand, or it disappears and reappears also in the thrower's hand? If it's the first one, you can make the guy who crafted the returning net feel like a dummy. If it's the latter, you can make him feel super smart. If you feel it's OP you could outright prohibit it, or just right up and allow it always (if the net teleports back, it could teleport the caught target too), or you could do an interesting mix, where upon first use it fails but the user realizes that with a small tweak in the enchantment he could upgrade it to dragging the target back.
In cases like these I think it makes no sense to try to fit the game world into the mechanics, but instead to fit the mechanics into the game world. Whatever's most fun, or whatever prevents the players from getting too distracted, or whatever fits previous rulings best, or whatever other strategic choice you might favor instead.