My iPhone 13 is making a constant static and crackling noise even when turned off and shut down

Try a Forced Restart on the phone. Follow the instructions very carefully, as this is a bit tricky. (Hint.....ignore the "slider" when it appears and keep holding the Side button in until the Apple logo appears. This might take another 30 seconds.)

Force restart iPhone - Apple Support

There are only 2 possible results when you perform a Forced Restart:

1) The phone returns to normal operation

If the phone continues to make the static noise......

2) There is a hardware problem with the phone that will need attention at the Apple Store (make an appointment) or take the phone to an authorized Apple Service shop.

You can find a list of authorized service shops in your area using the link just below:

Find Locations

The Apple Store is always a good choice, but an authorized Apple service shop might be closer....and faster.

Your decision though.