I just saw Romain Bardet in the live stream of the Tour de France stage. In the image, I can see there is a box-like form in his back.
What is it? Is it maybe a transmitter for the radio to communicate with his team?
It is the body pack for the radio. The body pack contains the antenna (or more precisely, the antenna attachment), receiver, transmitter, microphone preamplifier, headphone amplifier, and all the other electronics that make up a modern digital two-way radio.
Here you can see a cyclist demonstrating all components of a typical cycling-oriented two-way radio pack: radio body pack, headphones, throat microphone, and push-to-talk button.
Source: https://retevis.com/rbc01-bicycle-riding-gmrs-two-way-radio-bundle
This is the first image / product I could find. The body packs used by top-tier pro cycling teams would be a lot smaller, thinner, and lighter, and would have a flexible wire antenna or even one integrated into the casing of the body pack instead of the thick, fixed rubber stub.
Also, sometimes the lead rider of a team could maybe not have a PTT button but instead their microphone would always be open, so that the entire team hears them all the time. Same for the rider in an individual time trial. This is basically to free them from having to press the button.