usualy there is no need to have the audio being routed through your video chain. It is common practice to have them separated until the point, where they are streamed. This could be OBS on the same machine where Isadora runs (without audio through it), a separated computer or a hardware streamer like a Aja Halo. Only on this final point they get married and streamt right away. You might have to manage some latency issues by delaying audio or video on some point, to have it syncronised. This can be done by OBS or some hardware delay devices.
It is the same for live TV productions or any other, stream or recording.
The only reason to have audio going through izzy, would be effects or generating them from there.
Best
Dill