I read this as the engine runs poorly when not loaded, which is effectively idling, at rated speed. Likely, the engine surges/hunts when unloaded.
This would, IMHO, point to a deficiency in the idle fuel circuit, or an air leak in the intake train, possibly at the throttle butterfly bushings, or between carb and intake at the cylinder.
Consult the tecumseh L-head service manual for clues on cleaning the idle passages of the carb, once you've id'd your particular model.https://www.allotment-garden.org/rotavator-manuals/Techumseh-L-Head-Engines-Manual.pdf
When re-installing the carb, double check any gaskets downstream of the carb (from carb to engine).
Also, if you opened the float bowl when cleaning the carb (Of course, you did!), replace its gasket with new. They are not reusable and WILL cause issues if not properly sealed.
I'm guessing your machine has fixed Hi and Lo jets (not adjustable), but if they are adjustable, it may be as simple as an over-lean idle (LO) jet.
Should have you sorted.