Wash the mower & engine best you can.
As you can still start the engine that eliminated a rod hanging out the side of the crank cases.
This leaves a few possibilities .
1) blown lower oil seal.
This will have the floor of the engine bay clean and oil dripping down the crank shaft onto the transmission drive pulley from where it will be flung everywhere
2) blown crank case gasket.
This will have oil all over the top of the engine bay floor but nothing above the crankcase split line
3) blown head gasket
This will have oil dripping from the block onto the engine bay floor
4) blown top oil seal
This will toss oil every where all over the engine because the fan will blow it every where.
5) leaking breather.
Again throws oil every where but very rarely will toss out a large amount of oil.
Find where and there are plenty on here who can fill in the why.