You can think about rhythm apart from the saxophone, I call that internal rhythm. Within your body and/or directly transferred by something like drumming.
When you play rhythm on saxophone, it often involves the movement of multiple fingers which need to sync up perfectly. So even if some of your fingers are on time, if they are not all on time, there are problems.
I found a rhythm game online which uses one button and was built to be very precise.
Try it out and let me know how far you can get and/or if you have any questions. I made a video of myself playing through ‘world 1’. I make a few mistakes but get through it.
It starts off fairly in a fairly approachable way.