Not sure on Mac side, but I've read of OBS Projector mode
depends on how you are capturing/displaying that pre-recorded content
Are you using a Media Source or VLC, and direct using that in OBS? ie Video not displaying else and being captured
If exact time sync isn't critical, you could display the live stream monitor (so would have the typical 15->45 second delay)
or the Projector type option (basically take the stream content and output it to a video out port, then use that to drive a display)
In my scenario (House of Worship), I am constantly alternating between pre-recorded content and live video camera feed of priest
I use speakers attached to OBS PC and set Audio to Monitor and Output so we all can hear the pre-recorded content (no regular attendees)
I use Exeldro's Media Controls plug-in so I can watch/monitor time remaining on the video
(as I use Advanced Scene Switcher plug-in to auto switch scenes when video is over to Live camera shot)