Your starter motor is a dc series motor. The armature and field are fed by the same connection, that M connection on the solenoid housing that powers up when the solenoid is operated by the key switch or starter button.
Such failures of starters are not uncommon, and a good shop can repair them...often with parts
from a similar starter that has failed in a different manner that they have repaired in the past and have in the shop, or that an owner has decided to replace with new or remanufactured starter, or with new parts
they can order.
Find another electrical
shop. That starter should be easily repairable.
Then find out why you have rust on your starter. You must have a leak somewhere nearby...perhaps on the engine
cooled?) that is so small that the mist is hard to see, and perhaps only leaks
when the engine is hot.