Star Trek lore (not Lore) question

We're in the habit of bouncing around between streaming services -- turning them off when we aren't using them, turning them back on for something specific, forgetting to turn them off again... One of our on-and-offers is Paramount+, since the only shows I care about on there all have Star Trek in the name. I'd seen the first two seasons of Discovery and kept meaning to get back to it, but somehow I never did and suddenly I was two seasons behind. Finally, the release of Picard S2 inspired us to resubscribe, but for long story reasons we haven't actually watched that yet; instead, we watched Lower Decks Season 1 (and so far the first episode of S2) and I got back to Discovery - I've now watched the first 7 or 8 eps of Season 3.

I'm enjoying it, but something about the lore has been nagging at me, something I don't dare look up because I'm sure any site that might be helpful would also be full of spoilers, not just for Disco S3 and S4 but for Strange New Worlds. So I come to you, my faithful DW friends, for answers. It's about the Andorrians and the Orions and their relationship to the Federation. A bit of context first: my Trek fandom has always been centered around the TNG era -- mainly TNG and especially DS9, but I've also seen all of Voyager and the first two or three seasons of Enterprise. However, my knowledge of the TOS era is reeeeeally shaky -- I've seen some of the movies, and a very few episodes, but I don't have the lore at my fingertips at all.

As mentioned above, I'm hoping to get this answer with no spoilers for Discovery S3 or S4, or Strange New Worlds (or Lower Decks S2, if that happens to be relevant). But feel free to spoil anything and everything about TOS -- I recognize the statute of limitations is long up there.

( Behind the cut for Discovery S3 spoilers )

Many thanks!