To test your diagnosis, try this. With the bowl removed, but the float installed properly, hold the carb level and gently push the float upward. That’s is where it would be if the bowl was full of fuel. The plane of the float should be more-or-less level when it stops.
With the float at the top of its travel, blow gently into the fuel inlet tube (you might want to use a small bit of new clean fuel line for this). What SHOULD happen is that you won’t be able to blow without letting the float drop a bit.
It’s the same principle as the float in a toilet tank. When you let the float drop, that should open the valve as you blow.
If you CAN blow through with the float at the TOP of its travel, I’d suspect that the tiny rubber o-ring , which should be in the seat tube, is gone. That will prevent the needle from closing tightly, thus allowing fuel to keep flowing. You’d be best off buying a carb rebuild kit, or at least the gasket set, to get that o-ring. Note that o-rings for carbs must be specific for fuel, meaning that o-rings for plumbing will deteriorate more quickly.