iPhone 15 and iPhone 16 turning off simultaneously

If you connect your iPhones to an Apple 20W Power adapter and the USB cable which came with the devices, do they show any sign of charging after connecting them for at least one hour?

Restart an unresponsive iPhone - Apple Support

If the iPhones still won't start, you will have to get them serviced by contacting Apple or visiting an Authorised Apple Service Provider near your place:

Contact Apple Support - Apple Support

Apple - Find Locations

1. Follow the Apple article to resolve the issue --> If your iPhone, iPad, or iPod touch won't turn on or is frozen ...
2. If not resolved; please follow the steps in the following link for support with this issue: If your iOS device restarts or displays the Apple logo or a spinning gear unexpectedly
3. You still see a black screen after charging, force restarting, following the steps in this article.
   1. You see a black screen, but you can hear alerts, sounds, and vibrations.
   2. The screen remains black, but the device chirps when you unmute it and connect it to power.
   3. Your screen is on, but it doesn't respond when you tap, slide, or try other gestures. 
   4. You can't force your device to restart because a button is broken or stuck.
   5. Your device is stuck on the Apple logo, displays a solid color, or isn't recognized in iTunes.
   6. Contact Apple Support to set up service if you have any of the above issues:
4. Please follow the steps in the following Apple Video for support with this issue:

If none of the above steps resolve the issue, it is recommended to reach out to Apple Support or visit an authorized service center for further assistance. They can provide specific guidance based on your device model and iOS version.