I have the same exact problem too, and if anyone has better explanations for it please tell me too, but, since my cat is 6 now, and this has been going on since she was a kitten, here’s what I’ve noticed:

First things first, cats often (but not always) shit outside of the box as protest.

For mine, it most probably had to do with how clean she thought the sand was.

Mine was always this way when I also had that closed box, as well as when I was using silicone sand when she was still small, but without the box.

It’s only recently, that I’ve gotten normal bentonite sand (clumping pee, easily fully removed), an open box (ventilation), and clean the sand almost always daily, that she has almost stopped. And when The Depression hits and I forget to clean it for 4 days or so, she does all the things mentioned, I’m assuming out of desperation, to make the bad smell go away.

Silicone sand needed to be fully replaced, and the box be thoroughly washed often, because it would at some point stop being able to contain the ammonia smell.

The closed box, I noticed, would both, contain and absorb bad smells itself, as well as incentivize me to not clean as often, since it didn’t bother me when it would start smelling a bit 😐, but the cat had to be in a shut box, faintly smelling the ammonia for many many seconds.

Full disclosure, bentonite sand has a few studies correlating it with cat respiratory problems, probably due to the dust that cheap bentonite has packed in. I’ve decided that it’s still probably for the best to buy bentonite with its dust filtered out(slightly more expensive), since it helps incredibly with cleanliness (if your cat has to groom unclean paws, that’s going to strain her kidneys and liver probably).

Also, the sand is both extra useless weight, and makes cleaning harder, because it clumps worse. The more expensive brand, where they remove the dust, makes everything easier, and probably much healthier.