What causes this weird digital feedback sound in recordings?

I was shooting a meeting and at the meeting, they have a council. Everyone in the council has a microphone at their seat, and all those microphones get pumped out to the speakers in the room. It also gets sent through the ceiling i'm guessing, because I plug an XLR cable into an audio out XLR port on the wall in the back of the room to get sound for my camera.

I noticed actually during the meeting, this sound was coming through the speakers at the meeting, as well as the headphones on my camera as i was monitoring the audio during the recording.

does anyone know what causes this so I can try to avoid it happening in further recordings?

It sounds to be some electronic device in the building causing interferance, which would take time and effort to track down. If that is coming through the speakers in the room, yeah, that's interference. Probably not "modern" cell phones, could be, probably an older cell phone, or something else in the building.

It's interesting it appeared to start when she pressed the button on the "wireless presenter", and continued for about 20 seconds. That might be a coincidence, or maybe that remote briefly woke up some corresponding equipment which was mis-wired.

It is probably a wiring or grounding issue on their equipment. They have an audio amp and either integrated or separate mixer. The fact it came out the speakers plus appeared on your XLR feed from their system shows it's (1) On their end and (2) The signal got into the amp vs just appearing on a single output.

When shooting video it shows the benefit of having a backup separate audio source, e.g. on camera shotgun or audio field recorder.

I haven't looked at the spectral diagram but it's possible this could be fixed or reduced in severity using Izotope RX4.

Highly doubtful RX will help. I've been there with these types of systems, a lot.