What does "GC" mean in the patch notes?

Could even be GAC if they forgot the "a"
...and we all know how good they are at proof-reading

In this case, I think both of them.
Inquisitorious enemies will have this modifier in Conquest.
Inquisitorious allies and enemies will have this modifier in Galactic Challenges.

Is conquest known as Galatic Conquest?

The new Galatic Challenge starting in a day and a half, has Inquisitorius bonus. So it'll be 'challenge'.

GC is Galactic Challenge. Conquest is never abbreviated (at least not by CG).

Both Conquest and the renamed "War" are under Galactic Battles, but Conquest is never appropriately referred to as Galactic Conquest. You will occasionally see some players erroneously use "GC" in place of "Conquest," though this can create confusion as GC normally means Galactic Challenge.

They consciously left the "Galactic" out of Conquest before releasing it because they realized "GC" was an abbreviation that already fit too many things. I vaguely remember a post about this.

If you tap the (i) icon next to Conquest and War though, the titles do say "Galactic Conquest" and "Galactic War".

GC is Galactic Challenges. It came first.

Although its technically Galactic Conquest, CG always refers to conquest as conquest, and so does the community afaik

Haven't seen anyone call Conquest, GC except in this thread

They should leave the "Galactic" out of Legend too, since Galactic Legends aren't really that, except JMK.