Is there a way to search/filter by safeness?

There are some preset filters on the bottom of the page like Trending, Popular, etc, and there is one for “verified”, but there is no way to filter by safeness, that is, the permissions the flatpak requires to work.

It would be nice to have some improved filters to search for that…

No filters like that would be too complicated. You would have to rank each permission and their combinations somehow.

That rank is already implemented on the page of the app, there are three icons to specify that:

So the idea is to use the same logic for the filters.

OK, I assumed you wanted something finer than that. That one currently covers a wide ground, so there will be a lot of apps with the same rank.

Yes, may be even adding “safe” as a badge on the search results would promote those apps a little bit.