Since I don't use my RV over the winter months, my process for storage for the past couple years has been to fill the fuel tank completely, add stabilizer, and run both the Ford and generator engine enough to ensure the stabilized gas is through the system. I then fire the Ford and generator engine for an hour or so every month or 45 days until used again. That's worked well.
My generator was one of the first (in early 2019) to have a fuel shut-off valve installed in the genny fuel line as standard by Phoenix (or so they told me). I haven't used it to run my generator dry each time, but I do think that can be a useful help given the design of the Onan carburetor.
I've done a lot of small-engine work, and have repaired/rebuilt/replaced numerous carburetors used on Briggs, Tecumseh, Kohler, Kawasaki, and other engines. Using the "run-dry" approach for storage on most of them won't hurt, but is not really a totally effective approach. The Onan carburetor has a unique design that I think is what makes it so sensitive to fuel problems with stagnant fuel--as well as allowing the "run-dry" approach work on the Onan. Most bowl-type carburetors have the main jet and actual fuel pick-up point in the fuel bowl located some distance above the bowl bottom. That means that whenever you "run those carbs dry", there is still residual fuel in the bottom of the bowl that remains to go bad since you don't actually get all the fuel out of the bowl. That also means, though, that they're not as subject to problems from tiny bits of contamination on the very bottom of the bowl. If you will look at your Onan carburetor, however, you will see that the main jet and adjustment needle is a horizontal affair located in the absolute bottom of the fuel bowl. It essentially pulls fuel off the very bottom of the bowl. That means that ANY deteriorated fuel or residue at the very bottom restricts the jet and fuel pick-up--so the Onan is highly sensitive to any type of poor fuel and pretty easily can give fuel problems. Conversely, however, when you run an Onan carb dry, you're pretty much getting all the fuel out of the bowl, so it's more likely to be a successful technique with the Onan than with many other engines.
By whatever method (stabilizer, running, run-dry, etc) you especially need to prevent fuel deterioration (especially with E-10) in the Onan carb.