Is there such a thing as 'eBike specific' freewheel? I've recently had the LBS replace the freewheel on my eBike after 500 ish miles of riding.  The sprockets were not worn out, instead the freewheel bearing (not the hub bearing) had become loose.  It looked like this was due to the bearing cup loosening on it's thread.  My attempts to tighten it were futile, the LBS appeared unwilling to even attempt to do so, rather assuming that it was due to a low quality part.

They also claimed that it might be because it was not an eBike specific freewheel.  Does such a thing even exist?  If it does, what about an eBike makes such a thing necessary?

I challenged the LBS on that claim.  They say the freewheel sees additional load.  For a mid drive eBike that might make sense, but for a hub drive I don't see how that's possible.
I agree with you that a hub drive e-bike should not impose any more stress on a freewheel than a conventional bike.  Whichever wheel you drive, the torque supplied by the motor is not going through the freewheel.  The torque transmitted by the freewheel is all generated by you, just as on a conventional bike.  A stretch would be to claim that you can generate lots of torque in short intervals, then let the motor drive you in between, while on a conventional bike you would have to be working all the time so the torque peaks would be lower.