I would turn off the water supply valve for a couple hours and see what happens to the water level. If the water level drops, I wonder if bending the flush lever arm toward the wall would give a more centered pull on the flapper.
Also, that flush valve seat looks like it could use a good rub down.
One more thing that can sometimes make a toilet run; too high of water pressure. There are pressure gauges with a garden hose thread available locally for under $20. Those can screw on an outside faucet, laundry hookup, or the drain valve of the water heater. Over 80 PSI is excessive.