Can the app silence my phone during prayer?

Phones

Yes on Android. iPhone does not allow it — use a Focus mode.

Android

Silent Mode During Prayer lowers the ringer around each prayer and restores it afterwards.

Android

In the appOpen Silent Mode

Android

Set it globally or per prayer, with separate settings for Jumu'ah and Taraweeh.
Choose when it starts relative to the prayer, and how long it lasts.
Android asks once for Do Not Disturb access. Without it the app can only vibrate.

Android

In the appGrant Silent Mode Access

iPhone