What you want is called "Auto Generator Start" but it is usually included on coaches with an inverter and starts the generator when the coach batteries drop below a set voltage.
I'm sure there is one available that would start on 120Vac loss (or you could just use a 12V supply from the 120 to provide the 12V loss signal to a standard controller).
Seems to be a lot of information on this here:
https://www.rvtechmag.com/electrical/chapter10.php
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