Well, these carbs are fairly famous for being finicky, easy to clog and hard to clean. Not ensuring the float chamber is completely empty before storing is inviting problems.
You might try opening the float chamber drain screw, releasing the fuel and then spraying carb cleaner into the float chamber.
It's easier to do if you remove the drain tube from the plastic nozzle on the side cover. Do that a few times then finish by spraying WD-40 up there and close the drain screw to let it sit a while. That will sometimes free up a stuck float.
Have you tried pumping the primer bulb and opening the throttle half way (might need a helper to do that) as it dies? If not, try doing that first to see what happens.
If no joy there then pull the spark plugs and have a look.
I would probably just try a new set anyway. Look closely at the metal rings that attach the wires to the plug tips for damage or signs of corrosion.
Before putting the plug wires back on smear a very thin coating of dielectric (tune-up) grease on the inside of the boot to seal out moisture.
All in all though, this still sounds like a fuel starvation issue and might involve sediments in the bottom of the float chamber from the leftover fuel in there.
It could be a cold start enrichment problem with either the "manual choke" for pull only or the SE valve for electric.
But I would need to know which it has before telling you what to look for there.
Good luck.