I run dry, change oil, nothing else. Leave mulching cleans the deck, oak is like knifes. Been doing this for 50 years.

Running dry and removing the bowl for the last few drops is the best way. I would also drain the tank or fill it to the top. Keep your mower inside a garage or other covered storage area away from humidity, insects (esp dirt dobbers), and rodents.

I've always run it dry, but I don't drain the bowl. On the tractors with the fuel pump, I have been leaving the gas in, with treatment.

Either run unit dry or refill fully with fresh fuel with conditioner (Star*tron or Stabil) . Clean the engine and deck interior and exterior to prevent rusting and lubricate all joints and cables , store out of the elements as best you can .

I run it dry, but Idon't remove the carb bowl. I also drain the fuel tank. Clean or replace if necessary the air cleaner & spark plug. Sharpen the blade so it's ready in spring.

Next I squirt a few drop of oil in cylinder and pull rope several times to lube cylinder walls and rings.

I hand tighten the plug and then pull the rope just to the point where I feel strong resistance, this is top dead center. What this does is two fold, First it takes the tension off the valve springs, and second it prevents condensation from entering the cylinder since both valves are closed.

In the spring I remove the hand tightened plug and dry it off, then pull the rope to expel the oil. On startup it smokes a little for a short time then clears up.
Been doing this for over 35 years and it works for me.

I use Stabil in the gas for the last few mowings.
After every mow, I fill the tank to the very brim to reduce the dead air space to ZERO. That way the tank isn't "breathing" moisture laden air in/out with the temperature changes.
My 24? year old Honda took 2 pulls last Spring.