I love the concept! The writing stands out too—very catlike.
I found myself tripping over the mix of mouse & keyboard controls (I wanted to click to place things, or click away to close the laptop, etc), but I see you're already aware of this.
I also struggled with the pace a bit. Maybe with more time it'd be possible to have more assets/content to make the off-time easier, i.e. animations to watch (unique animations for each toy, cat-trait-specific animations for common things like using the litter box or eating, Pixie getting up to various things, outside weather, some hypnotic music visualizer wobbling in the background, etc), sound effects to spark imagination (particularly ambient ones like wind, rain, children outside, traffic, etc) and music to nod along to. The fast-forward button helped a bit (and I appreciated that the fast-forward seemed to stop when there was an arrival or departure to deal with). Another way to deal with the off-time would be to add other interactions. We could help keep the old lady fed and rested (it was a bit alarming watching the clock roll through the wee hours while she stood in place, staring at the wall—if only she could nap and trust her furry business partner or caretaking instincts to wake her should something go wrong). We could engage in idle low-stakes interactions (misting plants, maybe, or knitting cat booties, or periodically looking out the window to get a text description of what neighbors/passersby were up to). Or routine interactions go be expanded into multiple steps (maybe cleaning the litter or setting out food produces trash/recycling to put away, or putting water/food in the bowls requires bringing a pitcher/bag to the dish. I know the time constraints of a jam really limit things, but since you mentioned you were thinking about continuing work on this (and it's just fun to think about) I thought I'd write up a few ideas.
As a jam game it's impressive how much you've put together here. There are some nice emergent moments in the simulation, like when bringing in a new cat you might happen to notice one of the others is feeling lonely, so after letting out your new visitor you stop to pet the lonely cat for a bit before returning to the task at hand (i.e. taking the crate to the storage area). It's cute and it feels good. There's also just something about the departure routine that's just adorable and makes me smile every time, something in the way the cat just climbs right into the crate after you set it down.
Well done!