Phone has a green screen despite the color underneath,

Perform a Forced Restart on the phone. Follow the instructions very carefully, as this is a bit tricky. You may need to repeat this several times.

Force restart iPhone - Apple Support

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

1) The phone returns to normal operation.....

or, if the screen is still acting up.....

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

It seems like a hardware issue, but let's try this first just in case it fixes it. Restart your iPhone. To do this, do volume up, then volume down, then hold the side button till you see the Apple logo.