So I'd been fighting with this for a while before coming on here, and posted it when I didn't see anyone else with the exact same problem - but as a I suspect it's at least related to the full trash cans bug, I read through that thread after, experimented some more, and I think I found a work-around you can try:
1. Get the NanoCan. (I had to use the money cheat to give her enough money to afford one)
2. She still can't throw anything out, but I can drag-and-drop to the NanoCan.
3. Once the NanoCan had eaten a few piles of fur, I was then able to drag-and-drop to the cheaper trashcans I'd had from before. She still couldn't throw anything out.
4. I found and removed (via drag-and-drop to the NanoCan) every bit of trash on the lot.
5. Five minutes later, when the cat used the litter box, she was able to clean it - and has been able to use the NanoCan a few times since (though... I don't think it gave her any money? That's fine though, since she shouldn't have been able to afford it anyway). I haven't played very long to see if this will last, nor do I dare use any that need to be emptied, but at least I'm un-stuck and able to play this lot again! I'd recommend trying the NanoCan & a manual clean-up if you have the same issue.
Edit: Yes, this work-around has continued to work for a couple Sim weeks - it hasn’t gotten stuck again on this lot. I’m just using the NanoCan though.
