Looks like the Android 8.1 update brought along a new issue with it. Over at the official Google Pixel community, a lot of users have been complaining about slower screen wakeup response for more than a week now. Specifically, users - majority of whom are Pixel 2 XL users - are complaining that post the update, whenever they try unlocking their device through the fingerprint scanner, the device's screen wakes up after a significant delay. Some say they observe the same behavior on pressing the power button as well. Turning on the 'always on display' seems to have fixed the problem...
Source: https://www.gsmarena.com/google_pixel_users_say_android_81_has_made_devices_screen_wake_up_response_slow-news-28755.php