Rebuilt armed trawlers as offshore patrol vessels

How would an old armed trawler be classified if rebuilt with only a new power plant and sensors?

It would probably be an offshore patrol vessel; making it the equivalent of a monitor would require much more extensive modification.

A rebuilt armed trawler with new propulsion and sensors would be an offshore patrol vessel. Those changes improve mobility and awareness but do not supply the combat capability associated with a monitor. Reaching that standard would require substantial additional work rather than a limited machinery-and-electronics refit. A ship's role depends on its complete fighting system, not simply the age of its power plant and sensors.