Dialing from MacBook shows that my iPhone is already on a call
tl;dr A reboot of the phone fixed the issue.



When I tried the same on my iPad (making a call through my iPhone), the same thing happened, I received the error message that my iPhone was already on a call. This showed that the error seemed to be with the phone, not with the MacBook.

I closed all open applications on the phone, but ended up with the same error again. After finally restarting my phone, it worked, I was able to initiate a call from the FaceTime app on the iPad.

It looks like something on the iPhone prevented calls from being initiated from another device. Phone calls from the phone were working fine throughout the day, just not from another device.