Temporary commit to check the version mismatch in netbeans ... don't judge!
Jersey setup complete, the trick was to initialize and use jersey following the documentation at : https://jersey.java.net/documentation/latest/deployment.html#

I was trying to register the jersey servlet at the server level, which would have required copying jersey, javax.ws and many more dependencies to the root
of the war file, because the webapp context is not yet initialized at the server initialization phase, so WEB-INF/lib jars are not scanned.