My series 20 has that engine. The carb was leaking through and filling the crankcase. Installed an in-line fuel shut-off and a couple of oil changes later it seems all good. Hopefully it turns out to be as solid as yours.Mine has a 14HP I/C Briggs with the cast iron cylinder liner. She's a keeper.
One of the reasons I like the Kohler is they have a spin-on oil filter. But they are stupid expensive and don’t seem to be available in this horsepower range anymore.