In the end it’s mostly an agreement on how moderation actions should and are allowed to propagate for activity pub groups, which you can learn more about here https://codeberg.org/fediverse/fep/src/branch/main/fep/1b12/fep-1b12.md#group-moderation
The tl;dr is there’s a set way of saying these specific users are allowed to send actions such as delete on these specific posts, and software that implements groups (communities, to lemmy) ideally implement it in the same way. Of course, someone could always make a software that denies all remote moderation actions for instance, so it’s always up to those implementing the AP spec.
Lemmy has a large userbase, so generally probably gets to decide a lot of these things, such as how moderators are listed when getting information on communities, and other software will have to choose to follow along to be able to work with the large userbase or raise concerns/give feedback if needed
It’s one of my big projects, in progress in this PR. I’m really happy with where I got it to recently. I’m not sure if it’ll make it into 1.6.0, but it’s what I’m currently working on.