If you come back before end of August you can still keep your allowed stay with a re-entry visa to get before leaving Thailand. Then you'll ask for an extension when you're back.
Private hospitals usualy do the job with the immigration on your behalf, it is part of their public relations service. (not only for covid related cases.)
Home quarantine only if you come from red flagged provinces. Doesn't apply if you go straight from ASQ to airport. A friend of mine arrived in Hat Yai last week with no issue.