I'm noticing there's an errors spam when entering play mode. This may not be the only reason why things aren't working, but the console should definitely be error-free before we can really start solving the issue
Looks like your InputActions in ThirdPersonPlayerInputsSystem is uninitialized, which causes a nullref exception
If you haven't already seen it, there's an "Online FPS" sample here that covers how to setup a networked game, how to use the new input system, how multiple players are handled, etc...
https://github.com/Unity-Technologies/CharacterControllerSamples
There is documentation specific to this project here:
https://github.com/Unity-Technologies/CharacterControllerSamples/blob/master/_Documentation/Samples/onlinefps.md