This is my Monday morning dance of Bluetooth. 99% of the time I'll join a call and everything is connected, line levels are set and yet... No audio. I know people complain about Pulse but MacOS is just as bad and, seemingly, getting worse.
Perhaps the parent poster user AirPods. Those in contrast would seamlessly switch between your iPhone and MacBook . Apple more or less by planned design nowadays work seamlessly with their own products and their support for other devices is patchy .
On contrast, my linux laptop does not have any issue with the same headset and it gets connected instantly.