Mary:
I've used Airpods Pro 2 with Repeaterphone. They work, but I don't like
the way the microphones of the AirPods sound on calls through
Repeaterphone too much. The built-in boost Wes added helps some, but
it's just not my favorite way of using it.
You can tap the push-to-talk button on-screen as normal. Headsets won't
change how that works.
I don't have Shokz, since they don't work that well with my hearing
loss, so can't comment on that. Apparently, the Shokz OpenCom has a
pretty nice microphone, but, again, no personal experience there.