Single engine pilot reported a NMAC while approaching a non towered airport.

Narrative

Flight in IMC from ZZZ1 to ZZZ to practice approach and grab breakfast. On IFR flight plan for duration of flight in communication with ATC. Arrival to ZZZ requested RNAV XX at ZZZZZ ZZZZZ1 ZZZ and cleared for approach and switch to advisory with no other traffic observed. Reported ZZZZZ RNAV XX inbound to ZZZ 12 miles south of approach Runway XX. Reported ZZZZZ1 RNAV XX 11.5 mile final for XX. Heard traffic for a helicopter in the area that had departed and no other reported traffic on advisory frequency. No ADS-B targets observed or visualized from other pilot in right seat either. Reported 5 miles final; 2 miles final; short final (inside 1 mile) RNAV XX full stop. Observed Aircraft Z waiting to depart ZZZ at hold short line. At 300-400'agl observed Aircraft Y approximately 300' ahead approaching Runway XX no radio calls heard and no ADS-B target observed on equipment available. I performed a go-around for Runway XX and asked for receive report from area traffic. Aircraft Z reported loud and clear and asked if that guy in the Aircraft Y was with us since we were both tail draggers? I replied no he isn't. I asked if they heard the traffic in question report on frequency which they replied they did not. I extended downwind for Aircraft Z for their departure and landed uneventfully. Questioned pilot of Aircraft Y when we reached the FBO building about where he was from and events. He reported from ZZZ2 and ZZZ3. He stated he was going to go to another state today but weather was too bad and flew to ZZZ instead. He stated he recently flew the airplane from where he had purchased the airplane. He denied hearing traffic in area but claimed to be we ADS-B out and talking/listening on frequency. He promptly returned to his aircraft; taxied out and departed. Review of arrivals and departures on Flight aware from ZZZ does not show aircraft in question arriving or departing the area.