I have always viewed StaBil as “one season” treatment. I’ve seen gas treated with PRI-G siphoned from a motorhome after 8 years, put in a car and run fine - but this was early 2000s so probably no alcohol.
I buy alcohol free premium for power equipment, and as much as possible for our vehicles. Funny WinterDeere mentioned a splitter; I ended up repairing the carburetor on my splitter. The little ring that is the seat for the float valve had swelled. So yes, unless it’s just going to sit for a day or two, we shut off fuel and run it dry. Same for our generators.
Experience leads me to believe two cycle oil includes stabilizer. But best practice for chainsaw storage is fuel tank dry, oil tank freshly filled. A few years ago, I had a gal who worked on saws for a living tell me that with today’s gasohol, if you’ve mixed fuel and the can is two months old, throw it away and mix new. Over 90% of saw engine problems she saw were due to fuel.
I’m sure ethanol free lasts longer in the cans. But if the dated label on the can says it’s older than I like, I’ll often put it into my low compression 1959 Massey Ferguson and let it mix with the gas there.
it is possible to separate the alcohol, if you need small amounts of alcohol free and can’t buy it. But it’s a chore. A friend with many older machines (his rag washing machine is a 1915 Maytag with kick start gas engine) sometimes buys avgas for a machine that will be sitting for a while - but he pays around $10 a gallon at the local airport.