Okay I will answer it as written for now. As I mentioned in a comment, Purebloods already get poison immunity, so you are actually giving them one new ability, which is the Serpent's Tail thing. Instead of comparing it to the loss of magic resistance - which is clearly stronger - I will just compare your race to usual PHB races, so you can know if the race is balanced overall.
It is certainly weaker than the Yuan-Ti and probably weaker than usual playable races.
As usual (when I say as usual, I mean I always do it), I will be using the point system from this guide to classify whether a race is good, bad or average. This guide is quite popular on the interwebz and has been proving a great tool for me since I discovered it.
I will start with the standard points and then make some adjustments based on my experience.
You get the usual +3 ASI, so that's three points. Assuming you are keeping the Darkvision from the Yuan-Ti, that's another 0.5. Speed and size are both the common 30 ft and Medium, so no points here.
The guide gives +1 point for Damage Immunity/Resistance, and you could think the immunity to poisoned condition should increase that somehow, but from my experience, both the poison damage type and the poisoned condition are fairly rare, thus it remains at +1. So far you got +4.5, which puts you in par with Halflings and Dragonborns.
Before continuing, I would like to state that the ASI here is a little trappy. +2 Charisma, +1 Intelligence, while accounting for +3 ASI, is not as good as, for example, +2 Str, +1 Con. The reason is that no class can efficiently combine Charisma and Intelligence. This is one of my main criticisms to this guide (which puts standard human at +6, which is extremely optimistic since it's probably the worst race in the game because no class effectively uses the 6 stats). So I am reducing that +3 to +2.5, sorry.
Now, your Serpent's Tail. Note: I assume the constrict is an usual attack, i.e., you have to roll the attack and beat their AC for it to hit, similar to how monsters' Constrict attack works.
From my plays with Aarakocra, the truth is: we're rarely going to use the Natural Weapon, unless we're desperate. From a damage perspective, there is no actual reason to hit with 1d6 + Str instead of 2d6 + Str or simply 1d8 + Str if you want to use one hand. The "target can't breath" will be mostly pointless 1, as any character can stand for at least 6 rounds without breathing (described in the Suffocating subsection in the PHB), and from your wording it would be able to breath when you fail the attack roll. And being fair, most creatures being targeted will be dead before 6 rounds.
1 Okay, there was some clarification here: it's ruled that no breathing = no verbal components. That makes it considerably stronger, but I am not sure how often spellcaster enemies will get caught by this feature, and this is a house ruling so it's hard to make a balance judgement here.
Overall, for most builds, your feature does little and is worth about +0.5, putting the race at +4.5, which is the lower-end of the spectrum, but obviously playable.
A comment on your feature when put together with the attributes from Yuan-Ti
In particular, Charisma and Int are not the attributes I want for a character getting a melee attack based on Strength. The best class I can think that would benefit from the Charisma and the melee Str attack would be a Paladin, but I would probably still take a Dragonborn or Dwarf instead of this homebrew. So, even though the individual features are worth +4.5, the lack of synergy between them makes it hard for me to think on a good character to put them.
The Hope: Grappler Build
HOWEVER, this feature is amazingly interesting for a Grappler Build. Usually, what you want to do is: Grapple and Shove. One of the main weaknesses you get from playing a grappler build is that you lack damage because you are using your Attack action to, you know, Grapple and Shove instead of, you know, doing damage. Additionally, since you are usually using one free hand for the Grapple and another for the Shield (Shieldmaster Feat, Shove as a Bonus Action, also +2 AC and +2 on Dex Saving Throws doesn't hurt), you can only make Improvised Weapon attacks with your shield (or Unarmed attacks, depending on how your DM rules), which results in a low damage output even after you successfully grappled your target. This feature mitigates both of these problems well, as you can attack and then try the Grapple, and you can attack while grappling. Constrict is usually a Melee Weapon Attack, so it gets advantage on attack rolls against prone targets - this seems sweet.
One problem is that, the way you worded it, Constrict is a specific action, not a part of an Attack, so you don't benefit from Extra Attacks. It should be fine as long as you build accordingly, or you could change that wording and allow multiple constrict attacks, I don't see it as being broken.
If you are playing with a specific Grappler build, I would give it a +1 for this feature. Really, having played grapplers, this feature is worth a (good) feat, mainly if you change the Constrict stuff. So, for this particular case, we get a +5, which is already fine, almost on par with Half-Orcs and Gnomes. The huge downside is that, as I mentioned earlier, the attributes you get (Cha and Int) are not the ones you want for the Grappler build, thus I'm giving it a +1 and not a +1.5 (alternatively you could think that I took away another 0.5 from the ASI if you are playing the Grappler build).
Note: Obviously, this build is subject to the usual problems of a Grappler-oriented build, such as having diminished utility against multiple targets and being quite useless against larger targets.
The main suggestion I would give to you is to change the ASI from +2 Cha, +1 Int to something like +2 Str, +1 Int. This would already make a very viable Eldritch Knight Fighter, which is a class that has no common races with a good distribution if he wants to focus on Str and Int, and that can make a good Grappler. This would bring the race to the a more average, even higher-side of the race spectrum, and give it a practical choice of class to see play.
I also suggest to try and keep the wording consistent with usual features from Wizards. For example, Constrict is a well-known attack from many creatures.
Constrict. Melee Weapon Attack: + 10 to hit, reach 5 ft., one
Large or smaller creature. Hit: 17 (2d10 + 6) bludgeoning
damage plus 17 (2d10 + 6) slashing damage. The target is
grappled (escape DC 16) if the behir isn't already constricting a
creature, and the target is restrained until this grapple ends.
The restrained condition is considerably more useful than the lack of breath, at least by RAW.
Finally, consider giving them some really minor trait just to give them that last +0.5. Maybe something with little or no combat influence, for example some Proficiency that makes sense in your mind, or a small speed boost (35 ft.) if you think it makes sense (except for the Bone Naga, the Nagas in the MM have 40 ft speed IIRC).