Single Pilot reported an engine stoppage during initial climb after a touch and go landing. Pilot advised tower and selected a grass area for a forced landing.

Narrative

I arrived at ZZZ Airport XA30 to begin preparing for my flight. Requested fuel of 20 gal in each wing; 40gal total. Even though I was only planning on flying about 1.5 hrs. Weather was checked the night before and conditions seemed VFR with overcast skies about 4000-6000ft. Checked again the morning of similar with high winds and gusts in direction of runway; and still VFR.Begun my pre-flight inspection according to my checklist i.e. inspect flight controls for freedom of travel; sump both main tanks after fueling; turned on main battery and checked pitot port heat; strobes; nav lights; landing lights; elec pump; all ok. Checked main gears for security of hydraulic lines; no leaks; brake pads; actuators and any abnormal wear and tear. Checked prop for nicks; dents; smoothness. Engine bay area for belts security of mounts; and oil level sufficient above 7 gal. As well as any other items on checklist e.t.c.Inside the aircraft; completed interior checks; sumped both lines from interior valve. At XC00 Cranked the engine on R tank; all indications normal; oil pressure; oil temp; fuel flow; amps; volts. Nav lights on for ads-b out e.t.c. Check the atis before taxi while engine is warming up.Taxid to a spot; asked ZZZ ground for clearance for taxi with westbound departure. Cleared for taxi to XXR via taxiway 1 crossing runway XXR. Taxid down taxiway 1; cross runway XYL; made it to the SW run-up area. Did my run-up checklist; flight controls free; mag checks; prop cycle; vacuum; amps; volts; idle check all green. E.t.c.Did my pre-flight checklist; takeoff trim; 15° Flaps; doors and windows closed. E.t.c.Asked for clearance for departure XXR with westbound departure; was given clearance with R pattern and departing the pattern westbound.Lined up XXR; heading lined up; elec pump on; landing and Strobe lights on.Full throttle; Airspeed alive; indicators all green; oil temp; oil pressure; manifold pressure; fuel pressure. 80kts start lightly pulling the yoke; liftoff positive rate of climb; 300ft gear up; and Flaps up; 2500 rpm and 2500 prop 700 ft start right crosswind turn. 1000ft right downwind turn and straight out the pattern.Flew to ZZZ1 for touch and go's; only one touch and go as ZZZ1 was closing for maintenance.Flew back to ZZZ called ZZZ Tower within 10nm with ATIS for the option; I was acknowledged and given XXR clear for the option; report 3 m final. Was called back within 7 miles to change runways to XXL clear for the option.Steady approach for XXL began my descent and pre landing checklist; ram air close; Cowl Flaps close; Flaps; landing light; elec pump on. Did my GUMPS checklist; gas set; undercarriage down and locked; mixture full rich; prop full forward; seat belts.I did realize I had been flying on R tank for about the hour and never switched tanks; so switched to L tank to balance fuel load close to final.Touched down XXL; all good smooth landing. Cleaned up Flaps check runway length remaining and decided for the touch and go. Full throttle; Flaps were already up; positive rate of climb. At about 150 ft realized I was quite low and prop started to slow drastically; started to bank left to come back to the airport. Prop stopped completely as I advised Tower and set fuel valve to OFF. checked gear was still down and locked. Looked for minimal traffic area on the road; but was too busy. Found the grass area looked clear and braced for landing.