I would suspect a faulty compression release.
A primer bulb, even missing, won't affect compression-Nor will clutch replacement (or lack of a clutch).
If you can post the full model # so we can look up your specific model:
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/husqvarna/chain-saw Looking thru the exhaust port (muffler removed) for any scoring will indicate
the general condition of the internals.. Any decent scoring will (up and down on piston/ cylinder)
WILL lower compression..
.
IE, A Stihl MS201 with a scored piston / cylinder