These radar lights usually do two things. They flash rapidly if a car comes too close to the cyclist and they also enable your head unit to display an indication of how far away the car behind you is.
So you kinda need a head unit to make the best use of your 100$+ light.
I've seen cyclists use it to know when they will be overtaken. They all like it but I've seen it only among cyclists who cycle as a sport.
It helps when the car is going real fast so you don't even have time to hear it or for people who don't want/can't look behind them to know if there is a car when they turn left.
With a radar you are never surprised so it can help some people to feel safe.
I don't think it changes how you react but how you anticipate.
Even then I don't have a radar on my bike. It's too expensive for my use case right now.