GA pilot reported an NMAC during approach to land when an aircraft on the runway delayed their takeoff. The aircraft on approach conducted a go-around and returned to land.

Narrative

Cleared for visual; with calls out from 7 SM; 5 SM; 3 SM and upon entering left downwind for 34. Aircraft Y in traffic pattern and announcement at midfield with no visual but on ForeFlight on the merge. Aircraft Y within 100/100 with Aircraft X diverting to south west and extending downwind; base and 2 mi final. Aircraft Y still on runway on 1 mile final which necessitated go around. Extended downwind; base and 2 mile final with Aircraft Y now on runway announcing 'touch and go' with no movement. On 1 mile final; Aircraft Y still not on the go. Aircraft X advised that touch and go was to go not to stop. Aircraft X diverted to the right overflying right taxiway. Aircraft Y elected to take off with both aircraft abeam the numbers XX; Aircraft Y at 3800 and Aircraft X at 4000 - safe separation. Aircraft Y left crosswind; Aircraft X extended departure; extended downwind; base and 2 mile final with landing. Aircraft Y Student pilot confronted Aircraft X pilot after landing indicating that Aircraft X did not own the airport and not authorized to instruct other aircraft; with Aircraft X responding that touch and go; precisely that; not a stop and what could both pilots learn from the situation.