Ideas
I have a similar problem on PC. At level 4, I started not being able to work or get a promotion. I used a cheat to level up to level 5. The cheat got me to level 5 but didn't fix the problem. My work days come and go without any notice. I restarted my game, deleted mods, tried other households. Nothing works. I also have a few book related bugs (not being able to drag and drop books or buy books from a bookshelf. The used bookstore in Innisgreen works.)
I have done some testing on a clean, redownloaded game without mods. New save, new family. I was Not able to get my sim promoted in the naturopath career past lever 7 by seeing customers at home. The promotion check lit up but after the shift, it would turn off and work performance would reduce a half a bar. I was able to get promoted by sending my sim to work although they hated it because it was indoors apparently. I also tried "working from home" without seeing clients and that worked as well. The problem I had was just with seeing clients. I have save files and videos if you need to see them.