The shop should be able to tell you why it won’t come on. An overcharge shouldn’t kill the compressor. It’s possible, but you probably weren’t that far over serviced that you would fluid lock the compressor
Some systems have a “self protect” that needs to be reset after an excessive high, or low, pressure was seen by the controller.
This often requires the manufacturer software. I would seek a second opinion on this.
And I doubt it was PSI they were talking about. More likely it was lbs of freon. My Mercedes and Volvos use Kg. But the shop machine might be graduated in lbs…