This is a known issue with the iOS version of the SYSTM app. While it worked fine in the SUF app, SYSTM unfortunately is not playing well with other audio apps in iOS and takes control of all audio.
However, I have found that by switching back and forth between my audio app and SYSTM I can eventually get my music to keep playing AND still hear the SYSTM sound effects cues. But it takes a little extra time an patience.
This is on the roadmap to be corrected, but since I don’t work for Wahoo I don’t have a date for you. I just know that it is a known issue and will be fixed at some point. Hopefully soon. Because it is definitely annoying. And yours is certainly not the first I’ve seen asking about this issue.