No Onan gen output

Do you have a VOM?

Those generators, if they fail to make voltage after they are started, will shut down and give a fault code pointing to the possible problem.

You might try turning off the breaker to the microwave and see if the generator works and provides AC power to the rig without the microwave. Just a step in trying to figure out the problem. If the generator provides power without the microwave determine what voltage the generator is putting out - might be too low to power up major appliance?

Look in your operator manual for location of breaker switch on gen. If that's on check at you ats with multimeter for power from the gen. Ats may not be switching.
Or as mentioned if its manual check the 30amp reseptacle you can also check for power there with your multimeter.

Your model may need to be plugged into the generator 120v, ac, outlet located inside the cord storage box. Did you remember to plug it in?

The generator also has a reset switch towards the right side of the unit.

I'm not sure why the microwave is flashing, but have you checked the breaker(s) on the generator itself, and in the RV's distribution panel? Even when they look OK, it's worth cycling them off & on to be sure they're not tripped. Also, some RV's require that you plug the shore power cable into an outlet powered by the generator.

Another issue can be that the GFI outlets(s) are tripped. Some outlets require a close look to see the GFI buttons.

Jim, "Mo' coffee!"