How about a pause mode?
I use Android's Bedtime mode a lot, and it has a helpful feature that let's you quickly "Pause for 30 minutes" or "Turn off for now" from a notification [1].
I don't think the app needs notifications as such, but it could have quick access to a pause button.
[1] https://img.gadgethacks.com/img/original/21/75/6372310031848...
I actually saw that exact feature on the app in a notification, with "pause for 30 minutes" and "turn off for now".
Ah perhaps the app is using bedtime mode for its functionality? Didn't get a chance to try it myself yet, but great that pausing is already implemented.