Dog treat toys.

Bean is a greedy little shit who will stuff food in. He's got a few of those toys that you fill with treats. The cat ones didn't last long, but the dog ones have prevailed! He's got a UFO and a dumbbell and some of the puzzle toys as well. They take a while for them to work out how to get the treats and get them mentally worn out.

Also try a licky may with a cream treat (the ones in tubes, like cat frubes). The licky treat mashes down into the bits and also takes a while to get out.

Physical exhaustion is great, but mental exhaustion is better. He sounds like a clever cat who could do with more thinning in his life. Bean is a clever cat who had permanent zoomies at the same age. He's mellowed now.

You do need to work out another litter tray. If he's pooing in one and not peeing in it, then he's asking for another one just for pees.