Well, streaming software works differently than giving FB app, or a browser session local camera access. But, to simplify, yes, you describe what I've been doing for last 4 years... but really, such 'profile' consideration is NOT something OBS Studio is aware of or does anything about
OBS Studio sends using Stream Key, and that key is tied to a given Page/Profile. Which Stream Key uses dictates where the video goes.
I'm still using the older FB /live/producer. Note the option to use 'local camera (via browser) or use Streaming Software. Naturally, with OBS Studio, you use the Streaming Software option. I use Scheduled Videos as that allows non-FB users to watch video simultaneously without logging into FB (with a consistent URL for every video).
- For security, I choose to NOT use a Persistent Stream Key, so our workflow is to log onto /Live/Producer, create/connect to appropriate Scheduled Video Event, grab stream key, and off we go. Being aware of need to stream in advance of Go Live time (as noted on FB web page).