The Kohler 10 horse and 12 horse engines use the same crankshaft and rod..... which means the stroke is the same. What differs is the size of the bore.
Kohler decided to cast blocks with extra thick cylinder walls. Some blocks were then bored for the ten horse pistons while other blocks were bored for the 12 horse pistons. The only way to figure out the HP of your engine is to remove the head..... which is not a big deal....and should be done anyway periodically to remove carbon.... and measure the bore diameter.
As noted, Kohler also made many different oil pans to bolt up to their basic engine blocks. All engines came with a SPEC or Specification number noted on the ID tag. Manufacturers could SPEC which oil pan they wanted, which alternator coil amperage, whether they wanted a starter/generator or an alternator/starter and if the engine was to be on gasoline or propane.
If the oil pan obviously does not fit the frame of your tractor then it is equally obvious that the engine has an entirely different SPEC and it came from a completely different tractor. If it works, then it does not matter UNLESS..... you intend to conduct a proper restoration. At that point, you need to seek out an engine from the same model tractor as you have.
Checking the crank output side of the block for the identifying mark in the casting means nothing because many of the K-241 blocks became K-301 blocks by way of the boring bar at the time of manufacture.