We should start to get a basic collision and health system going on. Here's how it might work:
Each Player (not the Car) should have health which ranges from 0 to 100. This value must be synchronised across the network using the same technique used for 'PlayerName' and 'IsReady' property in Player.
Connect the Player Bar to the Health, so the Bar length changes as the health changes. Perhaps if <50 health then the bar should turn orange, then <20 health bar should turn red.
Some basic collision system, where ramming other cars results in losing some health. Do not worry about calculating how much health lost, just make it some constant value like 20 for now. Ensure that only the car with the higher velocity loses health on collision. Detecting collisions can be done using OnCollisionEnter() placed in the PlayerCarController script. The collision should be done so that a player reduces their own health if their velocity is lower than the collided game object's velocity.
Do not worry about player dying, just make sure health cannot go below 0.
We should start to get a basic collision and health system going on. Here's how it might work: