How do I fix an unresponsive iPhone with notifications but a black screen?

Do a forced restart.

1. click the volume up followed by the volume down botton rapidly
2. then after clicking the volume down botton immediately hold the power botton until the apple logo appears, keep holding even when the screen goes black

Force restart iPhone – Apple Support

You don't hold down the volume buttons, you quickly press and release them to do a forced restart.

• 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 button.

Force restart iPhone - Apple Support (IN)