profiteer The OLED display now has the green tint issue, the phone is almost always warm and very, very slow to use.
There are many reports of "green tint" being a hardware problem, over multiple years, with multiple device types.
Here is just one: https://www.ifixit.com/Answers/View/732171/Extreme+green+tint+-+Pixel+4+XL
And, interestingly, here is a report that includes excessive heat while the device is on: https://www.reddit.com/r/GooglePixel/comments/18o9kpj/comment/ku6tr3b/
If you have any developer options on, you could try turning them off (this is basically always a good idea), and if you have any color-changing settings in effect (Night Light, special color profile) you could try changing those. But unfortunately the description sounds a lot like a hardware failure.