Pilot reported fuel starvation caused engine power loss during climb; resulting in a return to the departure airport and a precautionary landing.

Narrative

This marked the first flight of this aircraft in over 2 years after an engine overhaul that simply took longer than expected. This first flight started with an engine start-up; a warm up in the Run-Up Area of ZZZ at Runway XXR; with a positive all-systems check and run-up according to the check-list; a subsequent high-speed taxi on Runway XXR and after a final check a careful first flight of a box-climb to 4;500 ft. directly over the ZZZ airport. The new engine performed flawlessly during all of these trials and all indications were good until the engine experienced loss of power and I was unable to get it to run with full power again. I called ATC and reported the loss of power along with a request to land back on Runway XXR which was granted by ATC. I descended; turned base-to-final and landed on Runway XXR without incident but with a stalled engine and couldn't exit the Runway until I got a requested tow from Operations Truck from ZZZ. Upon thorough inspection it turned out that the cause of the loss of power was fuel starvation and that there was no more remaining fuel in the airplane's tanks; while upon take-off there was an indicated 37 gallons remaining; which; under normal flying conditions and a 12.5 GPH fuel burn should've provided an almost 3 hour flight time; but my flight time was no more than 30 minutes. The last time I fueled the plane (top-off) was a 12 gallon fill-up back in 6 months ago; after which time the Fuel Totalizer had indicated 40 gallons available fuel. Trying to figure out how this was possible; either the plane lost fuel between the last fill-up that did not get indicated on the Fuel Totalizer; or the last fill-up was in fact not a fill-up.