[BUG] Team Admin does not have to be member of the team

That's not a feature, is it? :D

Can you provide any pictures of examples of this happening that would be quite helpful.

Well you can just add any user to the list of admins. You can try it by setting up a new team and adding me, for instance :D

example: I added LordFinzenz here lichess.org/team/lichess-discord--httpsdiscordappcominvitepvhanhg

This is a known bug: github.com/ornicar/lila/issues/6494