I was surprised to find a +20 approval buff on all systems labeled as VR amaeteurs, after assimilating the Z'vali.

Just want to know if this is how it should work.

I don't think this is limited to Z'vali. Playing as Unfallen I have noticed that the +5 per Guardian approval is affecting every system in the empire, not just the ones they are in. Four total Guardians are giving me +20 approval in every system.

Some stuff is surely meant to empire wide - the collection bonuses, for instance?

VR Amateurs is one of their assimilation traits and is supposed to effect your whole empire. It's not related to the happiness boost from the actual pops. You can see what the assimilated trait does in your empire overview.

Guardians are likewise working as intended. They give two different happiness boosts, one is local and one is global, you can see they are clearly distinct on your happiness breakdown.