The bulb is not getting firm and I don't feel fuel going through. Now my starter is spinning but not engaging the flywheel.
When in doubt, I replace the bulb and any fuel lines in question. Bulbs have check valves which can fail. The rubber becomes stiff with time (and gas drying out the rubber). I consider a primer bulb a 3-10 year item depending on if gas has ethanol in it or not.
The other issue can be fuel pump (diaphragm tears and pumps into crankcase) and float not sealing which is usually trash in the needle valve but can also be a float not floating (filling with gas) or leak in the bowl. You'd see a leak in the bowl.
Fuel pump diaphragms get stiff with age and eventually tear (leaking into the crankcase through the impulse hose). You can rule a leaking fuel pump diaphragm out by plugging the fuel line directly to the carb inlet and pumping. If it fills the bowl and shuts off, it'll firm up the primer bulb.
You'll unfortunately have to refresh some parts on your engine before it's useful. But it'll be worth it if you have good compression. I'd put a little 30 weight oil on the starter bendix and work it by hand up and down (with battery unplugged of course) a few times then just let it sit oiled. It may come back. If not, probably will need thorough cleaning.