Persistent notifications in notification bar (e.g. countdown timer, stopwatch)?

I'm trying to decide whether I should create a React Native app at this point or if I can wait a little longer.

My app has a countdown timer showing how long is left of the current task. I want to show a persistent notification when the timer is active and has time remaining so I can swipe down and see how long it will be before the next notification. I might also want to embed actions (e.g. Done or Add 1 minute) that would cause actions to happen in the background.

But I'm not sure if PWAs even have the concept of running in the background. I'm not that experienced with them yet and am at the stage where I'm thinking about if it's worth it or if I should go straight for a mobile app.