I’ve been pondering if I have knowledge here that might help. I used to work for Apple but not since Mac OS X Mavericks, so things have changed under the hood considerably.
It works if the entire desktop audio is captured, but not if application specific.
I do see you are using OBS’s Window Capture for audio capturing. On Windows this is marked as “BETA”, not sure about the Mac OS variant of OBS, but I can confirm on Windows the “Window Capture” and BETA audio capturing under that, is capturing Brave. (But you’re on Mac, so let’s try something).
I’m going on the assumption Mac OS still uses Core Audio, and um…gonna be honest I’m guessing here, but try this. Do not enable audio capturing under Window capture, so leave this actually unchecked:

Instead, add a dedicated source for simply capturing application audio separately such as this one (if it’s on OBS for Mac that is):

From there you can tell it which browser and window (it won’t follow the window capture, so you have to tell this source the same information you told Window Capture).
Does that work? If not, it’s the only thing different I see you doing that @Mattches seems to have done slightly different, as he used this:

(Based on the icon in their OBS capture that is, which is essentially screen capture’s method of capturing audio, the whole system, not just Brave, which you said did work, as application audio capture source has a different looking icon.)
Again just a guess. But if mattches did test “Audio Output Capture” and not “Application Audio Capture” (again I’m going on the icon I see being a generic speaker, not a speaker in a window), do you (mattches) mind re-testing that?
I think there may be a misunderstanding on the OBS side.
Audio Output Capture, simply captures the audio stream going to the DAC itself (overly simplified, but yea), whereas “Application Window Capture” captures the audio stream before it reaches Core Audio (or on Windows, WASAPI’s “mixer”).
However, since OBS does say on my side it’s “BETA”, it might be an OBS issue (since it’s a bit of a “hack” to capture audio before it’s mixed by the sound mixer of the OS itself).