A pretty classic problem. At least the wheel hasn't done the other thing they sometimes do, which is turn back into petroleum.
An IBM 5100 in my collection has a gripless wheel like yours: on that machine, I can press the tape cartridge firmly in the drive and force better traction. If I were less lazy, then I'd do what YouTubers like CuriousMarc and Jerry Walker do, which is replace the wheel. For his HP tape cartridge drive, Marc knows a certain kind of rubber tube IIRC that he can cut into rings that serve as replacements; he might also paint on some kind of rubber goo that widens the wheel and dries to something grabbier. Walker also starts with a rubber tube, but I think he fits it onto the post and then machines it down to the correct size in a lathe. This may yield a rougher, grabbier surface.
Good luck!