There probably are no codes - the 112-120v range is well within electrical standards. The Onan would shut down if the voltage was outside of the acceptable range, and set a code if it did. If it doesn't shut down, then no code.
It is normal for the voltage to drop a bit under 120 with no load. 112 is a bit more than I might expect, though. And the fluctuating rpms suggests an engine fuel feed problem as well. It is not uncommon to have the carburetor get gummed up with fuel residue if the genset is not used regularly (at least monthly, under load). Some carb cleaner, e.g. Seafoam
, may help.
Do you exercise your genset every month, per the owner manual? 30-60 minutes under moderate load? If not, you should.
What happens when you run the genset and have an a/c on to give it some load? Does it smoothly increase speed and produce a steady voltage in the 115-120v range? If not, what happens?
The Onan service advice is very conservative. I doubt if you need a major overhaul yet. Maybe not ever. 500 hours is not a lot of usage for a genset.