Engine turns over when quick start is sprayed into carb…then stops within seconds…does not appear to get any primed fuel even though priming tube looks fine

I bet you've parked this over the summer with fuel in the tank? Correct? If so the carborettor needs cleaned... you have gummed up jets.

When you pump the bulb do you hear a sqush of fuel and a bit of resistance? If not the dip tube may have deteriorated which is not uncommon.