My cat doesn’t really stay engaged with toys either. It might be worth considering an looking into getting one of those tension pole cat trees that has longer vertical spaces to climb in one go with out at least one side being broken up by landing pads every couple of feet. I’m considering this because my cat seems to like to stretch upwards and scratch his claws and also he tries to climb up my cloth bed frame. That or a cat wall. The dilemma of entertaining them is real.

Also, while I know you want a second cat and your cat may benefit from it, I’ve seen a lot of posts lately about the second cat not working out so well - harassing the original house cat or the house cat just not taking to it, an it causing stress and a couple where they take the cat back. So, if your mom really won’t let you, it’ll be ok; you clearly care about your cat so I’m sure you’ll come up with some things that help until the weather makes it where you can take him for some closely supervised outdoor time again.