Coach battery seems drained after using generator.

IF your batteries charge when on shore power but do not charge when the generator is running ( same power cord )

You need to check the generator voltage output, and control board
it may be too low for the converter to do in any charge output

The converter should be charging when the Onan is running
The Onan is using 12v power for the electric fuel pump
But it should not be pulling down the batteries to the dead point