The super-short version as I recall it: the Gith were slaves of the mind flayers in ancient times, revolted, and fled into the Astral Plane where they split into two cultures, the Githyanki, who went full asshole in their endless crusade against the mind flayers, and the Githzerai, who are more the lawful-neutral monk types. Githyanki are the ones in BG3.
So yeah, they're mostly a Planescape thing (I want to say Planescape: Torment had a Githzerai party member), but they pop up now and then elsewhere.
the gith can be involved anytime the illithids are, so it's not just planescape. there was a point in time when the illithid basically ruled all the planes but the gith rose up and were able to fight them to near extinction. the gith queen made a pact with tiamat (because tiamat hated illithids too. pretty much everyone does) and allowed the githyanki to ride red dragons, which was one of the main ways they were able to fight the illithid.
the illithid are interesting villains specifically because they raise the question of whether or not it's moral to commit genocide. on the face of it, you want to say no, genocide is terrible. but if even 1 illithid survives they pose a very real, very serious threat. even your most morally staunch protector is like, naw, we gotta murder all them tentacles. the githyanki are cruel and harsh, but they aren't exactly evil, specifically because their entire purpose is the eradication of illithids in order to save the entire realm of existence from them. they aren't interested in conquest, outside of the illithids, so while they wouldn't think twice about killing innocent villagers, they have no interest in doing so (unless they have reason to believe they are hiding illithids).
it's one of the areas in which 5e shines, that they've mostly done away with alignment outside of certain places like the hells and the heavens that are intrinsically tied to aspects of alignment. it allows for a lot more nuanced interpretation on characters. though, let's not start the discussion on wizards of the coasts take on "oh orcs and draw aren't evil, they are actually the most morally righteous among us" nonsense.
Grabbit Allworth
knows what i'm talking about
also everyone talking about karlach, and honestly just barbs in general. wildheart is extremely strong, don't hate on it just because everyone says how wonderful berserker is. berserker IS great, especially since there's no exhaustion in this game (which in table top was THE reason not to waste time with berserker). bear totem.. uh.... heart... is the best tank in all of dnd. bg3 did lose some of the ancillary stuff that added to out of combat benefits to bear totem, but they also buffed the other animals as well. tiger being able to cleave every round is pretty great, especially with some of the weapons that are in the game. i'm not saying don't be a zerker, it's a significant upgrade to the table top, i'm just saying don't ignore the other subclasses