Radar and Standing Waves
This wave will return to the transmitter with a certain phase shift from which we can evaluate the distance between the object and the transmitter.


No. The radar sends a pulse, and times the reflection. It's the round trip time delay that's used to evaluate the distance to the object.

If you have a left-travelling wave and a right-travelling wave, then measure the total amplitude at various points with a detector sensitive to both waves, say a dipole and detector diode, then you indeed see a standing wave.

Although there may be a standing wave pattern when both waves are viewed like this, the two component waves are still there, they do not interfere, and each can be received separately. The radar receiver is set up with a reflector to receive only the return waves.