Prioritizing Tidying does not sweep up items on the ground without selecting them with a tool

I'm pretty sure the "storage" priority is the one that controls dupes putting non-swept debris into storage compactors.

Then it's wrong. The Tidy action states it covers Sweep, Mop and other actions aswell. In addition, this action gets prioritized by selecting a Groundskeeper job to a duplicant, so there are conflicting actions in the game.

Sweeping is a two-layered priority; you need to have both tidy and delivering prioritized. Tidy for the sweeping part, and delivering so that they can put it away.

Thanks again for your response. I then believe that applying for a Groundskeeper job should automatically prioritize Storage as their profession, because Groundkeepers are meant to clean stuff up. I actually put up a real bug now, third try's a charm.