Somewhat related question :
In a portable, gasoline fueled generator, should the tank be empty or full for long term storage?
empty, gasoline is corrosive (especially with ethanol)
Make sure the fuel lines are clean too
Some have steel tanks and others, like my Generac, have plastic. The metal I definitely would keep filled (that might be the only gasoline you actually end up having access to). The plastic is up to you. I keep mine filled, but evaporation does occur. Keeping a float bowl filled or not is another issue.
For long term storage (over two months), absolutely DRY, the engine run until it cannot restart or even fire as there is no fuel in the entire system. Then ensure the engine valves are closed (on the compression stroke) and SEAL the gas cap so no air can deposit its moisture.
Short term: absolutely FULL, with stabilizer, so no condensation can occur.
20 yrs as a small engine mechanic taught me these things. You haven’t lived until you smell a chainsaw with 3 year old fuel mix in it OY!