Jibri is the way to go https://github.com/jitsi/jibri but is quite some effort, requires separate VM with alsa installed, and that can only handle one stream
However, it seems only moderators can start a recording, which is not enough: also patricipants would need to be able to start a local recording, And the UX is a bit weard, if somebody needs to mix it later and there is no video.
SOLUTION: Open Broadcasting Software is a great streaming open source software: https://obsproject.com/
Download OBS on a (separate, performing) PC or laptop
Define as Source a browser and enter the conference room as URL https://fairmeeting.net/streamtest Remember, that the first user in a fairmeeting room gets moderator rights, so you probably should open this OBS capturing instance after you have opened it on the laptop of the event moderator.
In the browser settings, use 1920x1080 and route Audio to OBS
Right-click - interact so that you can click away the warnings, that no camera is attached to the OBS-internal browser. You may also switch on tile view.
Start your recording of the meeting
If you want to stream, define a streaming server from the list
For Youtube you need to get a key (see bottom of the Live Dashboard page, use link in OBS "Get streaming key"). Or use any other streaming platform or set up your own with nginx (see above).
You can save your configuration as a scene in OBS and open it next time simply on a command line obs --scene "myremoteliveevent" --startrecording --startstreaming
Thank you Jaromil for the hint with OBS. He was a former fellow of fairkom, we had set up publicvoice.fm 20 years ago!
Option Record Chrome Tab records audio from other participants, but not my own audio
Option Record Screen + Microphone + Speaker did not record audio from others, to be tested again @dimitri.hofer
Currently only works for the first recording, afterwards the sound of the speakers is missing.