I am interested in a way to capture audio not only from the mic, but also from one of the monitor ports so you could pipe the audio you are hearing from the web directly for real-time transcription with one of these solutions. Did anyone manage to do that?

I can, for example, capture audio from that with Audacity or OBS Studio and do it later, so it should be possible to do it in real time too assuming my machine can keep up.

Set -i 1 to -i default or to one of your monitors, look them up with pactl list short sources

https://trac.ffmpeg.org/wiki/Capture/PulseAudio