This seems rather obvious as a needed thing. I can certainly have separate processes for the feed to attach the window capture to, but, the main pulldown in window capture does not list all of them. Is it only ever possible to get what is currently focused? That seems insanely limited.
FWIW I posted about this yesterday, and since have done some experiments. Your post is quite old, and I guess OBS has been reorganised since then. But the basic problem remains I think. Maybe there is a plugin that can help.
Browser (actually Brave, but Brave is a fork of Chrome):
Version 1.67.134 Chromium: 126.0.6478.186 (Official Build) (arm64)
OS: macos Sonoma 14.5 (23F79)
OBS Studio: 30.2.1
Handbrake: 1.8.1
I opened a couple of youtube pages and had each one in a separate window. I could capture each window separately, but I could not separate the audio tracks.
Next I opened one youtube tab in Brave and another in Safari. I set up a scene with 2 "macOS Screen Capture" sources, one for each YT video. I set one tab to record to audio track 1, and the other to record to audio track 2. I then played each YT vid and captured 10 seconds.
I loaded the output file into Handbrake and processed it twice. Once with Audio Track 0 only and the other time with Audio Track 1 only. This time the output files had different audio tracks, one per browser tab. Handbrake will do video cropping too.
To do:
Check two Safari tabs to see if audio can be separated.
If so, prove that I can attach a macOS Screen Capture source to each tab and record both, even if both are not visible. but not minimised.