I Googled "android phone app to turn off phone" These are the returns:
1. The most commonly used apps to turn off or restart your Android devices are PowerMenu and Shutdown which are both available for free on the Play store.Dec 6, 2022
2. Is there an app that turns your phone off?
Turn off Android phones
Google's Family Link app allows you to schedule a span of time for the phone to be off, such as bedtime. But you can also completely lock the device so kids can't even get into it. Family Link requires two downloads, one for your phone and one for your kid's.Apr 19, 2019
3. Is there an app to turn off phone at night?
Meet Sleep Timer!
Sleep Timer lets you configure a timer for turning off any media that is currently playing on your phone. You can also sleep WiFi, Bluetooth, and even the Screen!May 13, 2019
4. How can I turn off my child's phone at night?
Download the Family Link for Children & Teens on your kid's phone (available for Android only). On your phone, create a family manager account. Once your kid's profile is set up, select Bedtime and set the span of time your kid can't use their phone.Apr 28, 2019
5. How can I control my child's phone from mine?
The easiest way to get remote control access to your child's phone is to download a parental control app. Before you can control your child's phone, you will need to create a profile for each child and then download the app on the kid's phone as well.
So it is possible for an app (like Poweramp) to turn a phone off (or any Android device) and it can also be done remotely, phone to phone, but I just want Poweramp to trigger a shut down when a song (or Playlist. etc.) has finished. These results tell me a standalone app can do it, so Poweramp should be able to incorporate it. Not based on a time setting, but when a song is finished. If it has to be time-based, then have Poweramp note the time on the phone and have it turn the phone off a few seconds to a minute later.
There are more returns from the search above about apps that can do it, so please get with the Poweramp app engineer/coder to have them research the best way to add the feature into Poweramp.