Is there a way to set up an “Active Provider” station, similar to how the logistics chest works?
If not, could you add one?

Not yet – there is no active provider station in UTL right now. It's a good idea, and I've put it on my list for a future update.

<3

To be honest, I had completely forgotten about this – sorry! Since 0.0.12 there is the role "Active provider" (checkbox in the station window). The station is then emptied like an active provider chest, even without a request: first to requesters, then to storage stations up to their maximum, finally to cleanup stations that accept the goods. The scenario "UTL active provider" shows it round by round.

<3 ^^

I believe I had achieved similar setups with LTN or other train logistics mods. Suppose your city block factories consume fluids in barrels, and you want to recycle used barrels by putting the used barrels into active provider stations that gets higher priority. However LTN's priority system didn't work well enough at that time and you ended up wastiing materials to unncessarily produce new barrels, so how to deal with this? The idea is to put the barrel recylcling on a separate networ, and you would need two different stations in your factory blueprints to obtain barrels: one for new barrels and one for recycled barrels, along with some global signal network to enable the "new barrel" stations only when there is too few recycled barrels in the network.