@OtaDr I'm not sure my experience is similar. My phone connects to a Bluetooth headset every day (Skoda car kit or Sena headset in my motorbike helmet), and I never noticed any issue with this.
Also, based on the test I made at the time, it's not that the ringing is silent -- the phone doesn't ring at all and the caller is immediately redirected to my voicemail.
Furthermore, I noticed something else during my holidays in France. In this case, my phone was roaming on a foreign provider's network (SFR), and the problem manifested itself again. I had to use the same technique to get the phone to ring again. So I have the feeling there may be an issue in the way the phone negotiates the initial connection with each new provider it uses.