Which live caption apps work without the phone's microphone?

For me, Live Transcribe allows either, selectable in settings. This is on a Pixel 8 Pro with Philips 9050 hearing aids.

Yes, I think that’s a special feature of the Pixel phones. It doesn’t work that way on my Samsung.

Not sure if this is what you’re talking about, but on my Pixel there is an ap " Recorder".
When you turn it on you can select audio or transcribe. I use the transcribe selection a lot when I’m at the doctors so I do not miss anything the doctor says.
I just push the transcribe button and put the phone in my purse.
When I get home I just go thru the transcription to be sure I didn’t miss anything.
You could also just lay it on the table and read it as you go along.
I’ve tried using it at restaurants, but didn’t care for it as it picks up everything sound and voice from all around.
Maybe this may help you ?

I do have Live Transcribe on my phone for situations like you described, but what I’m looking for is something that will do the same thing while I’m using my phone via Bluetooth with my Phonak hearing aids.