Personally their story seems a bit off to me. Depending on the size and type of turn, if a property was trashed I think $3700 would be a great price to get it back rent ready so I can't say I'm shocked to hear of the random 'break ins' which led to additional charges. We typically see full turns on 1300-1800sf homes run between $4-6k. That's what I would consider to be trashed and repairs would include a trash out, full paint, changing carpets, fixing broken fixtures, deep clean, etc.
Also as unfortunate as break-ins are, I think most would love to walk away with having a bunch stolen and it costing less than $500 to get back up and running. I don't know what could be taken from a vacant home that would only cost $488. Maybe a broken window and lock change or a used fridge and stove? Are they providing a line items on invoices showing exactly what was being done, do those prices seem reasonable? Are you being sent before, during and after photos or photos after the break in? Is there police reports to support their claims?
Best of luck on a the second half of 2022.