Why does my iPhone 13 turn on during the night?

If you turn it off with the charger connected, it may start up again. Learn to use Do not Disturb focus instead of powering it off and charge overnight so that housekeeping jobs like Photos curation and Backup can occur.

that is weird, have you tried to force restart the iPhone to see if the issues persist?

Press and quickly release the volume up button. Press and quickly release the volume down button. Press and hold the side button.When the Apple logo appears, release the side button.

You should, you really should.