Should I have my home professionally cleaned after I am rid of scabies? Is this haz mat cleaning?

Probably wouldn't hurt but this is not haz mat cleaning. You really need to deep clean upholstered furniture and carpets. Make sure you wash sheets and clothing in hot water, not warm. Congratulations on getting rid of this pest.

Deep cleaning, yes.

Hazmat remediation, no.

The CDC seems to think that you don't even need a pest control treatment.
CDC - Scabies - Prevention & Control