PA-24 pilot reported failing to notify TRACON of safe landing as requested following precautionary landing after experiencing a runaway propeller.

Narrative

I departed ZZZ on personal intro flight with 2 passengers; and contacted TRACON for flight following to ZZZ1 area and then return to base at ZZZ2. Approximately 8 minutes after departure; plane experienced runaway propeller (mild overspeed; loss of ability to maintain constant speed; and then locked into coarse pitch/low RPM setting). I advised TRACON of the problem; announced plan to return to ZZZ for precautionary landing; and returned to the field. Controller handed me off to ZZZ CTAF and requested radio call after completion of successful landing. I failed to lose enough altitude on initial approach with propeller unresponsive; and to avoid over-running the runway was forced to make a low-power go-around; with difficulty climbing. Several pilots in the pattern and on the ground observed go-around (Max RPM at full throttle was 1700 RPM) and low pattern and were aware of difficulty; and deviated to allow a quick and safe second approach. With low oil pressure and local pilots on CTAF and radio talking to me; I was in a hurry to taxi to safe place and shut engine down. Immediately a Mechanic working at the airport approached me and began discussing the failure and possible causes; as passengers deplaned.In the stress of the go-around; second approach and quick shut-down; I failed to contact TRACON to advise them of my safe landing by radio.If similar event happened in the future; TRACON should be able to text pilot and receive an acknowledgement of safe arrival; as cell phone data in ADS-B records for aircraft. Alternatively; offer phone number in lieu of radio frequency for later contact with TRACON.