I tried again yesterday and it wouldn't even turn up in the simulator anymore.
Later I managed to check out a much earlier version, implement a simple test intent there and have it show up in the Shortcuts app (slightly earlier commits had the same problem). Going back to my current working state and pasting the same test intent there, it suddenly worked as expected again. Now I tried figuring out, what made the behavior occur in the first place and replicated my steps from the first time around:
It happens right after trying to add AppIntents on the WatchOS target. They won't show up there and those on the iOS side will stick around for a while, even if all AppIntents code is completely removed. New intents added on the iOS side won't show up at all. A while later the zombified intents disappear as well, leaving the state I described in my initial post (intents I saw on the simulator there, were from before I had tried adding some on WatchOS). All subsequent builds have this problem. I tried deleting DerivedData, Caches, switching around Xcode versions. Nothing works. Now even going to my early commit and back again does nothing. Guess I'll just have to wait?
Somebody, please help :(