Had a coworker who had COVID. He described standard respiratory disease stuff, but in addition, described being more fatigued than usual when doing physical activity. Even walking his dog took a lot out of him.
Whether he's on the up-and-up, this looks par for the course. As far as I know, the WH hospital would be able to monitor his vitals (especially blood oxygen saturation) but also organ health just fine. That said, I would have wished that he be monitored some more. Then again, as expressed before, I find it difficult to believe that his doctors (who certainly know much about this disease's progression) would allow him to be discharged if it wasn't sufficiently safe for him to be.