C-172 pilot reported ground conflict with another aircraft during approach to land at a non-towered airport and conducted a go around.

Narrative

I was making a personal flight to introduce my young son to general aviation. The flight was made to and from ZZZ; which is a non-tower controlled airport. Upon returning to the airport; I heard a local skydiving plane in the air making calls regarding jumping activity in the northeast quadrant of the airport. To avoid the northeast quadrant; I overflew the airport at midfield; and descended on an outbound 45 to set up for entering the left downwind leg of the traffic pattern for Runway XX. I sequenced into the traffic pattern behind a Piper Voyager and ahead of a Stearman biplane. The Piper in front of me was slower; and as it turned onto the left base leg I reported via CTAF that I would be extending my downwind leg to provide additional spacing. The Piper acknowledged with 'thank you'. The Piper announced performance of what I heard as 'a touch and go landing'. I turned left base for Runway XX and made a radio call. I turned on an extended final for Runway XX and made a radio call. The Piper was still on the runway. I expected that the Piper would be moving to take off; it did not. I decided to perform a go around but did not offset to the right of the runway is typical because as I was concerned about potential conflict with parachute jumpers. I made another circuit of the traffic pattern and landed normally.I spoke with the copilot of the Piper later that day. He was upset with the proximity of my C172 to his as I overflew the Piper during the go around maneuver. He informed me that he and the pilot of the Piper were performing a stop and go landing; not touch and go. I mentioned that the radio calls from the Piper were weak and scratchy; and that I heard 'touch and go landing.' He mentioned that I should have offset from the runway; and that he would have the radio checked out. I agreed about the offset on a typical go around. The discussion ended amicably.In retrospect; it is likely that the Piper did report a 'stop and go landing'; but I was expecting 'touch and go' since there was so much air traffic in the pattern and around ZZZ that morning. I was caught off guard with a plane stopped on the runway and distracted by the prospect of conflicting parachute jumpers. I should have initiated my go around sooner (at a greater altitude); and considered the possibility of offsetting to the left instead of continuing straight down the runway.