I’m not sure about the best way to handle the bacteria issue but I think because you’ll be doing water changes w/the med regimen it will help alleviate to some degree the bacteria/cycle issue - many hospital/qt it’s not possible to cycle because they are often needed in an acute situation.
Is he using that fin any more than he was? I’m following along, I have a Tomini tang and he’s my favorite fish, so much personality. They are quite hardy, mine took a carpet dive last week and scared the life out of me but he didn’t suffer any serious injury and other than a scrape on his noggin he never slowed down. Mine is very easily startled and does not like new people all up in his face, I would recommend to the extent possible that you provide him something to hide in or behind while you are treating him as he will likely feel exposed/stressed which won’t help his recovery.
Best of luck with your guy and please update us as you are able.