I know that sources for it can be a bit unreliable, and there are many different versions of the stories. But kinda just looking for one big reference for all (or at least a decent amount) of the most popular Knights of the Round Table, their backstories, traits and lore surrounding them, etc.
Basically, just writing a story that's supposed to kinda be a modern retelling of some Arthurian legends (none in particular as of yet), and wanting to go a bit deeper and see what's out there.
Well, there aren't any "reliable" sources for it in a historical sense, because it didn't actually exist. Likewise most of the knights don't have singular backstories, because they change from writer to writer. That said, the best reference for what you're looking for is probably the New Arthurian Encyclopedia, by Norris Lacy. It's extremely comprehensive.