Hello,
when I contacted Apple Support, I was advised to create a test user with admin rights, then log in and check whether the problem still exists. The problem does not occur with the test user. I then logged in again with the normal user and the problem reappeared.
However, I have seen under Settings that there are other audio drivers than the Macbook microphone and the iPhone microphone that could be the cause of the problem. I opened the directory /Library/Audio/Plug-Ins/HAL/ in the Finder and deleted all subdirectories and contents. After restarting the Macbook, Facetime audio from the Macbook via the iPhone works perfectly again and the microphone in the Macbook does not cause any problems. The other party can hear me again.
I hope you can solve the problem just like I did.