I had another thought on this subject that I want to share - it's not just a matter of "matching" BG3 that putting the Gith into the PHB would make sense for - it's also a matter of making D&D more exclusively D&D. Any fantasy RPG can have Elves, Dwarves, Orcs, & Goblins. Only D&D can have Githyanki. They're clearly leaning into IP these days (and they oughtta, it just makes good sense).
That, and they seem to be adding psionic subclasses as a late-day addition - and who better to represent that addition than the Gith? BG3 is just the thing that makes it not a weird choice, and comes with a very large audience, but it's not the only reason to add the Gith.
(I'm not sure they WILL, but it's a good idea all the same).