Additives are generally snake oil, unless you know exactly what condition you're trying to address.

Also additives often don't combust well themselves, adding to the issue.

I suspect the old gas had 2 issues: it had already lost some octane because gas is volatile - it will slowly evaporate the most volatile compounds first.

Plus sitting gas attracts water out of the air.

What you describe is much like what happens when you get some water in the gas - these intermittent sputterings when a little of that water gets to the combustion chamber.

About the only additive I'd use in this case (that is, thinking there's a bit of water contamination) would be some form of alcohol. It has the ability to bind with both gas and water, so instead of a blob of water getting injected (or pulled through the carb), a tiny amount of water gets combusted with a lot of gas on every cycle. "Heet" is a common brand in the US.

Any kind of very high proof alcohol will work (90%/180 proof) - higher is better, as the remainder in the alcohol (that 10%) is water.

Yeah, this is one of the major plot holes in Zombie/Apocalypse movies.

You always have scenes of people siphoning gas from abandoned cars years later and it just wouldn't work.

Ready to use gasoline can't last a year, even when stored in ideal circumstances. Crude oil even has a shelf life of only so many years.

It's one more reason everything's going electric. Much easier and safer to sort out electrical storage long term than gasoline.