It looks likely that it is indeed the Chromecast (‘Media Router’) support.
There used to be a switch for it in Settings that was easy to find. I wonder if it’s been enabled by default due to an upstream Chromium change maybe? There’s a bunch of options relating to it in brave://flags but it’s not clear to me whether any one of them might shut it off completely.
So, I think it’s that, but I am not sure how to shut it off anymore and I’m guessing we’d need to fiddle with some of those flags to narrow it down.
This is indeed related to the Discovery and Launch Protocol, used by the Presentation API and Chromecast. Chromium 93 included a change which unconditionally enabled the feature, meaning our Settings toggle was no longer useful.
Can you confirm that you’re seeing this network activity prior to any Cast request?