The indirect, bluetooth microphones built into modern headphones sound utterly terrible. The mane reason is all blueth microphones are limited to the 20 year old standard, 8khz sample rate & lots of compression.
There's a rare example at 4:10 of all the most expensive headphone microphones. Even without any singing or music, they all sound terrible or at least $400 instead of $500.
The 1st problem is the microphone cable is going to be a 2nd cable. Maybe it could be farstened to the speaker cable.
Most boom microphones have a hole in the side of an earpiece.
Top of the line pilot headsets have an extension under the earpiece.