Ryobi problem
This engine is a low compression engine. It will gain compression when it runs (oil / gas).
You can replace the thick head gasget with a thinner one, but the gain is very small. The up side of this lower compression engine is you can start with a typical glow started. The big upsided is the cost is about 100 bucks converted.
The Zama carby locks up when dry. Bummer you took the primer bulb off. I have one that does exaclty what you are seeing.... just pour a bit of gas on the vent side of the diapham and you should start pumping again.