owner of 3rd unit of pixel 8 since it was released.
man first off, on photos you provided there are clear cracks on the screen protector which means there possibly was some abnormal impact on the screen and the body of your pixel. this by itself can be and very likely is the reason behind the issue you're experiencing.
in my current experience an incorrectly installed / defective screen protector can lead to unstable behavior of the screen/touch pad. such as frozen image, unresponsiveness and etc.
to deal or no to deal wiyh google supportz i advise you to sqeeeze thr most out of them scammers.
1st make sure youre device is still under warranty(https://support.google.com/store/workflow/14778556?sjid=8450900451805534884-NC) - you'll need to sign into a google account for this, doesnt have to be anyyhing special, you can open one just for this. plus you'll have to enter IMEI of your device on that page, which in case your sceen is not usable and you lost the original retail box, you can find on the sim-card tray right there where the simcard is, it's in super small font so might wanna use some magnifying glass.
2nd then if google respomse on warranty period is positove just proceed with what you see further(here try to pay attention and read carefully what links you click, as in my experience google made that process in a away where it is easy to get into a loop where links that seem intuitively correct to take you the next step, just take you back to where you started)
3rd upon successfull passing that puzzlle, you will be asked for an address where google will send a box for you to put your defective device into, stick a shipping label(also provided by google, usually by email) and finally take it to UPS office to be then delivered to some third party repair shop contacted with google to repair under warranty devices.
a few tips of personal experience. the address you give to google to send you the box for your phone sometimes for no obviua reason might be recognized as undeliverable (mine was, despite google eas able to send few newely bought pixels to it) I just used friends address then, and it worked.
last part is so far negative in my case is that a clearly warranty case where the battery got bloated to the point where it pushed out the screen so that it separated from the body and hang on the cable, my device was held at the third party repair shop for 2 weeks, and sent back to me exactly as i have sent it to them. and the warranty has expired within those 2 weeks. whitout any comments or questions from google. I am yet to contavt them to escalate this one.