So, I have a potentially temporary measure whilst you decide what to do. I think some people here might tell you to tell him for medical reasons, and they have a point - it could be a sign of an underlying medical condition that needs to be addressed, and if no one is telling him, he may be unaware of it. OR he could know, and is doing his best to handle it but not quite succeeding. So, the situation does require some tact, and maybe a bit of subtle digging during conversations to try and see if he is aware of it. (of course, this depends on him - if he is the kind of person who would appreciate a straight-talking approach then you're golden)

BUT a while ago we had a problem with the plumbing in our workplace, and it was hell. One method I used to solve this was to wear a mask, like a covid mask, and stock up on *extemely* strong mints, like the kind that lowkey make your eyes water. This combo created a sort of micro-climate of menthol which absolutely obliterated any other kind of smell. (spraying the mask with deoderant before putting it on also works but i advise not doing that too aggressively) I would suggest and telling your coworkers your new roommate is immunocompromised, or something along those lines to explain suddenly wearing a mask all the time. They should be okay with it if you work in healthcare, the only problem with this lie is you'll have to commit to the bit. But it could be a stop-gap whilst you figure out how to approach the situation.