Anything is just a wild guess now that you’ve added more details, but I’ll stand by my statement that the crank didn’t break because the seal was missing. And with the seal missing I don’t even see how the saw could be running long enough, if at all, to break a crank.
There needs to be case compression for the mix to transfer into the cylinder, and case vacuum to draw the mix into the case. The carburetor wouldn’t even pump fuel from the tank without a sealed case. Everything about a 2stroke engine is dependent on a sealed case. If you were to vac/press test the engine right now, it‘d read zero no matter how fast you pumped the handle. I suppose even though it being a massive leak, if you could get the engine started, the momentum of the piston could output more pressure and vacuum than can escape through the leak because it’s a big enough air pump, but I don’t see how you would have enough carb adjustment for the saw not to meltdown the first time you cut with it. She’d be screaming for mercy at WOT and then go silent. I’d like to know how many turns your H screw is turned out. You’re going to have to retune after repairs anyway so if you can count the turns it takes to bottom out the H needle (clockwise) and report back, that would be great.
How hard was it to start? Did you have to squirt mix in the carb throat for it to start?
If it’s not scored then there’s absolutely no reason the P&C needs to be replaced. Pictures of the exhaust side of piston and cylinder wall would help make that determination.
Were you cutting with the saw for this “20 minutes” or just trying to get it to run? You also said this saw “has very low hours of use”. Are these your “hours“ running and cutting with it with no PTO side seal?
We are getting into the territory of 2+1 does not equal 3. As in, the saw possibly being in service for “hours“, a missing crank seal, and a usable P&C.
Fug it, why deal with crank seals, just richen her up.
