American here, so probably ignorant AF, but how wet are your teabags exactly? Everyone I've ever seen make tea does exactly that: pull it out of the water, smash it with a spoon against the cup rim to squeeze water out, toss it in the trash. It's barely more than damp after that.

Are the tea bags there so very different from ours that there's enough water retained in them that it risks making your trash can soggy?

(Tone here is meant to be curious, not confrontational; honestly wondering!)