Sounds like you have some wacky routing.
Are you the one that broadcasts from a different app, and not directly from OBS? If so, then OBS only has one viable output for you, which is the Monitor.
I have a rig that uses OBS's Monitor as its only audio output, but it feeds a DAW, and not the destinations directly. That DAW also handles all of the mics and other audio sources, and drives several different destinations independently with different content, including live speakers for an audience, my headphones, another instance of OBS, and a few others. That other instance of OBS takes its feed from the DAW, and passes it through unchanged as its only audio source at all. In your case, that might be the actual broadcast app.
The only reason that the first instance of OBS connects to the DAW, is because it's playing videos. As mentioned before, my mics go directly to the DAW, not OBS.
A physical console would work the same way, and each of the loopbacks that I need to get audio between apps, would turn into an ordinary, completely separate sound card.
Don't try to save some cost by using a many-channel interface for this. The channel count might be there, but you'll pull your hair out trying to assign channels of that single device. Much easier to have a bunch of stereo things and that's all they do...provided that they're not so cheap that even their serial numbers are the same! (don't sort by price and pick the cheapest) Each app connects to its own assigned sound card: done!