Forget the multimeter
Go back with some jumper leads
The fastest & surest way to check battery connections is to bypass them, one at a time with known good jumpers .
Start with a battery ground directly to the engine near the starter.
Because ZTR wiring is exposed to the elements and in particular due drop and the wires are all crimped not soldered, water wicks into the wires and corrodes them under the plastic insulation where you can not see it.
And remember the solenoid itself needs a good ground , particularly is it has only 1 trigger wire and grounds through its body to the mower.