Hello Brittany and all,
Eventually I could find a root cause of this error. The "Call ... Using iPhone" feature relies on an audio device with a microphone on Mac.
Once a call is initiated from the Mac, the iPhone loops back all audio to the Mac, which seems to be logical to ensure that control over the call is kept on the Mac where it was initiated.
Not all Macs have built-in microphones, however, and this "gap" is neither handled in MacOS 11.2.3 nor in iOS 14.4.1
When the Mac has no mic connected, it detects that "something" must be wrong with the audio routing and the not-meaningful error message "Call Failed" is raised. The Mac then disconnects from the phone, but the phone does not disconnect from the Mac and does not hang up, keeping the call ongoing with no audio until it is terminated on the phone.
Since this is also a concern from a privacy perspective (phone not in reach + invisible call ongoing), I hope that somebody from the developer team will find this article and implement a bugfix soon. Thanks for reading & have a great day.