There have been several requests for OBS to do exactly that, but it hasn't happened yet.
Until then, you'll need to use OBS's Monitor to get audio out of it, as that's the only audio out that isn't tied up in a stream or recording. Then you'll need to send that Monitor to an audio loopback of some kind. This can be as simple as an unused physical device, while the meeting picks up the OS's monitor of that device - that's a loopback - or you can look up how to create a formal loopback in PipeWire, or you can go so far as to pipe it into a DAW like Ardour, do all of your audio processing in there, and then pipe it from there into the meeting.
PipeWire is new enough that the LTS release of Ubuntu hasn't picked it up yet, so I'm afraid I can't help you with that.
What I can do though, is attach a pair of scripts to this post (and a PDF flowchart of the main one) that I use to set up a meeting with two copies of OBS, Ardour for ALL of the audio (OBS doesn't have *any* except for the absolute necessity for things like video soundtracks and recording), and an open-source browser-based meeting:
Join a WebRTC video conference powered by the Jitsi Videobridge
meet.jit.si
You can look through that script and see how it works with the older PulseAudio and JACK, on Ubuntu Studio 22.04 LTS.
Here's what Ardour looks like, doing ALL of the audio processing for the entire rig:
Some of that is to generate a 20kHz sine for OBS to pick up and modify, using the Advanced Scene Switcher plugin, and then return to Ardour as a control signal. (OSC is in the works for Adv. SS, but not released yet; once it is, I'll change it to direct control instead of audio control)
This plugin will allow you to automate various tasks using "Macros". Macros consist of a list of conditions under which a list of actions will be performed. Examples and guides can be found in the wiki. Feel free to contribute! If you run...
obsproject.com
The
OBS Master Ctrl
and
OBS Master Play
channel strips (green color-code, for "playback") are connected to the same source, and their steep high/low-pass filters at 18kHz do a pretty good job of separating a video soundtrack from the control tone. Then a set of side-chained compressors and gates scattered around, use the presence or absence of that tone as a mute/unmute function.