RAW, scenario #1 is correct; after using your free creation once, doing so again entails:
- Expending a spell slot at some point by any means available as part of an unrelated action, restoring your ability to create the cannon
- At some later time (though that time could be an action immediately following a bonus action that expended the slot), you can again use your action to create the cannon
For comparison, look at features like the Conjurer's Benign Transposition, which don't explicitly tie the resource expenditure to the renewal of the ability:
Once you use this feature, you can't use it again until you finish a long rest or you cast a conjuration spell of 1st level or higher.
That wording is identical, except "cast a conjuration spell" becomes "expend a spell slot". The Artificer's ability is more flexible, merely requiring you to expend a spell slot by any means, but also more limited, since the Conjurer's ability can be refreshed with ritual casting between fights (it only requires casting, not a slot expenditure), making it effectively an "at least once per fight" ability for the majority of cases where you have a 10+ minute break between battles, since you can just spend 10 minutes ritual casting Unseen Servant after each fight.
But aside from the precise resource expended, it's the same: You have an ability that takes an action, cannon creation/teleportation, that refreshes on a long rest, or when you expend a spell slot/cast a conjuration spell. The Conjurer doesn't cast the spell and teleport simultaneously, they cast the spell and recover the ability to teleport. In neither case is there any implication that the expenditure of said slot directly pays for, or is part of, the action used to create/teleport (any more than the long rest would be "part of" your first free creation/teleport), only that the ability to create/teleport is refreshed by having expended the spell slot/cast the spell.
The general wording for all caster classes (including Artificer UA, and I assume the final version published too) describes casting as (specific text from Wizard, but wording is similar everywhere):
To cast one of these spells, you must expend a slot of the spell's level or higher.
So "you can't do so again until you finish a long rest or until you expend a spell slot of 1st level or higher" means "you can do so after you expend a spell slot of 1st level or higher"; casting a spell is one way to do that, but not the only way.
For contrast, compare to the the Artificer UA, where RAW would involve summoning the cannon using the spell slot, since the wording there was (emphasis added on "by"):
You can summon a turret once for free and must finish a long rest before doing so again. You can also summon the turret by expending a spell slot of 1st level or higher.
That phrasing makes it quite clear the cannon is created at the same time as the expenditure (prior text makes it clear the summoning itself costs an action), and that the expenditure directly fuels cannon creation, but the new phrasing from the official rules you posted changes both the timing (the cannon creation ability restores after slot expenditure) and the cost (the slot is expended by any means available to you, with the bonus of renewing your cannon creation ability).
This gives you some unusual ways to renew the ability in multiclassing scenarios too; a Paladin's Divine Smite expends a spell slot, so a Palificer (Artidin?) could create new cannons after smiting, without actually casting a spell. A Sorcerer/Artificer could burn a slot for spell points (which still isn't free; beyond the action cost, buying the slot back with spell points always costs more than you get from burning the slot).
To me, it seems clear that the major change in wording from UA to published rules was intentionally to change the balance and availability of the class feature. In the UA, if enemies destroyed your turret, or you commanded it to detonate, you could use your very next action to summon a new one by expending a spell slot. On the one hand, this increased the cost (the slot was otherwise wasted, and if you'd used your low level spells already, the turret became more and more expensive), but it also increased the availability; you could always summon a new turret as long as you had spell slots. With the new version, the cost is lower (the slot is used for something else productive) and fixed (expending a higher level slot got you a higher level spell, with the cannon renewal being a fringe benefit), but it's not always available (you're usually going to have to use an action or bonus action to cast the spell to renew the ability; if you use an action, that delays recreating by a round).
Response to arguments for scenario #2:
Korvin mentions the Primeval Awareness ability for comparison, but that ability explicitly ties the spell slot expenditure to the action/power being used:
you can use your action and expend one Ranger spell slot to focus your awareness on the region around you.
and ties the benefit and the degree of benefit to the slot, incentivizing choosing a higher level slot:
For 1 minute per level of the spell slot you expend,
By contrast, nothing in the Artillerist's ability ties the slot expenditure to the use of the ability itself (it's not an action, it's not part of the creation action), nothing says the expenditure of the spell slot is only for that purpose, and (indicating it's not intended to balance the ability, just limit how often you can use it), nothing ties the strength of the cannon to the slot used to recover your ability to create it. It just says "If you expend a slot, the power becomes available again."
The point is, when a non-spell power/ability burns a slot to activate it (e.g. Primeval Awareness, UA Artificer's Arcane Turret), it's pretty explicit that the slot is burned as part of using the power. When the resource that fuels the ability doesn't burn the resource directly, but is directly dependent on it (e.g. Storm Sorcerer's Tempestuous Magic), the exact nature of the relationship is spelled out in detail. In the case of Tempestuous Magic, it specifies it what sort of action is used (bonus) and when it is used (before or after casting the spell). The final published version of Eldritch Cannon is like none of those abilities, much like Benign Transposition bears only a passing resemblance to any of them.