First, instances do save that list internally, but the API is still being worked along with the apps themselves, so don’t expect all features to work quite yet. Secondly stop using alts to harass communities you don’t like. If you do not wish to see certain content, block that user or community. Read the rules again if you need to, https://mastodon.world/about.

A Lemmy instance definitely saves that data as an instance admin can access it through the DB. Not sure if this is exposed via API

Yeah, I’d love to have this capability. I used it a lot on the other site to find random things I upvoted but forgot to save.