Ok, I will answer as written at the moment. As I mentioned in a comment, Purebloods already get anti-poison immunity, so you give them a new ability, which is the thing of the tail of the snake. Instead of comparing it to the loss of magical resistance – which is significantly stronger – I will simply compare your race to the usual PHB races, so you can find out if the race is balanced.
As usual (when I say as usual, I mean I always do it), I will use the points system of this guide to determine if a race is good, bad or average . This guide is very popular on interwebz and has proven to be a great tool for me since I discovered it.
I will start with the standard points, then make some adjustments based on my experience.
You get the usual ASI +3, so three points. Assuming you keep the Yuan-Ti Darkvision, that's 0.5% more. Speed and size are both the common 30 feet and average, so no point here.
The guide gives +1 point for immunity / damage resistance, and you might think that immunity to poisonous diseases should be increased in one way or another, but After my experience, the type of poisoned damage and the state of poisoning are quite rare. It remains at +1. . So far, you've got +4.5, which puts you at the level of Halflings and Dragonborns.
Before continuing, I would like to say that ASI is a bit of a trap. +2 Charisma, +1 Intelligence, although representing +3 ASI, is not as good as, for example, +2 Str, +1 Con. The reason is that no class can effectively combine charisma and intelligence. This is one of my main criticisms of this guide (which puts the standard man at +6, which is extremely optimistic because it is probably the worst race of the game because no class uses effectively the 6 stats). So, I reduce this +3 to +2.5, sorry.
Now, the tail of your snake. Note: I guess the restriction is a normal attack, that is, you have to launch the attack and beat its AC to hit, in the same way that the monster constriction attack works.
According to my plays with Aarakocra, the truth is this: we will rarely use the natural weapon unless we are desperate. From the point of view of damage, there is no real reason to hit with 1d6 + Str instead of 2d6 + Str or simply 1d8 + Str if you want to use a hand. The "target can not breathe" will be mostly useless 1As any character can endure at least 6 rounds without breathing (described in the Suffocating subsection of the PHB), and after your formulation, he would be able to breathe when you fail the attack roll. And to be fair, most of the target creatures will be dead before 6 rounds.
1 Okay, there was some clarification here: it was decided that there was no breathing = no verbal components. This makes it considerably stronger, but I'm not sure how often the spell's enemies will get caught by this feature. As it is an internal decision, it is difficult to make a balanced judgment here.
Overall, for most builds, your functionality does little and is worth about +0.5, placing the race at +4.5, which is the low end of the spectrum, but obviously playable.
A comment on your article when it is associated with the attributes of Yuan-Ti
In particular, Charisma and Int are not the attributes I want for a character who suffers a Force-based melee attack. The best class I can think of who would benefit from charisma and The scrum attack Str would be a Paladin, but I would probably always take a Dragonborn or a Dwarf instead of this homebrew. Thus, even if the individual characteristics are worth +4.5, the lack of synergy between them makes it difficult for me to think of a good character to put them.
HOWEVER, this feature is surprisingly interesting for a Grappler build. Usually, what you want to do is: Grapple and Shove. One of the main weaknesses of building a grappler is that you do not suffer any damage because you are using your Attack action for, you know, grappling and pushing instead of, you know, inflicting damage. Plus, since you usually use one free hand for the grapple and another for the shield (Exploit Shieldmaster, Shove as a bonus action, +2 AC and +2 for Dex Saving Throws does not hurt) you can only do it improvised. Attacks with your shield (or bare-handed attacks, according to the rules of your DM), resulting in a small amount of damage even after you managed to grab your target. This feature alleviates both of these problems because you can attack and then try the grappling hook, and you can attack while fighting. The constriction is usually a melee weapon attack, which gives it an advantage over the attack jets facing targets on the belly – this sounds nice.
One of the problems is that, as you said, Constriction is a specific action, not a part of an attack, so you do not benefit from additional attacks. That should go as long as you build accordingly, or you can change that wording and allow for several attacks by tightening, I do not see it as broken.
Yes you play with a specific version of Grappler, I would give it a +1 for this feature. Really, after playing the grapplers, this feature deserves a (good) feat, especially if you change the Constrict system. So, in this particular case, we get a +5, which is already good, almost at the same level as the Half-Orcs and the Gnomes. The huge disadvantage is that, as I mentioned earlier, the attributes you get (Cha and Int) are not the ones you want for Grappler construction. So I give it a +1 and not a +1.5 (otherwise, you might think I removed another 0.5 from the ASI if you play the Grappler build).
Note: Obviously, this build is prone to the usual problems of a Grappler-oriented build, such as a loss of utility with respect to multiple targets and a great uselessness for larger targets.
The main suggestion I would make is to change the ASI from +2 Cha, +1 Int to something like +2 Str, +1 Int. This would already make a Eldritch Knight fighter very viable, a class that does not have a common breed with good distribution if it wants to focus on Str and Int, and that can make a good grappler. This would bring the race to a more moderate, even higher, spectrum and give him a practical class choice to play.
I also suggest trying to keep the wording consistent with the usual features of Wizards. For example, Constrict is a well known attack of many creatures.
Tighten. Melee weapon attack: + 10 to hit, reach 5 ft., One
Big or small creature. Hit: 17 (2d10 + 6) pummeling
Damage plus 17 (2d10 + 6) cutting damage. The target is
grappled (escapes DC 16) if the behir is not already constraining a
creature, and the target is restrained until the end of the grappling hook.
The restricted condition is considerably more useful than lack of breath, at least by RAW.
Finally, consider giving them really minor just trait to give them the latter +0.5. Maybe something with little or no influence in combat, for example a skill that makes sense in your mind, or a small acceleration of speed (35 feet) if you think it makes sense (except for the Bone Naga, the Nagas in the MM have 40 ft speed IIRC).