The freezing touch-input issue seems to trigger on Pixel 6 (Pro) devices that have an Accessibility Service running with canPerformGesture permission enabled. When this permission is enabled, the whole system freezes for 1-2 seconds every time when the battery drops by 1%.
To fix it:
Go to Settings > Accessbitliy on your Pixel 6 and turn off every accessibility service you find in there, including Voice Access, Accessibility Menu, Switch Access, and others
Developer:Fix it if need on your Pixel 6 (Pro).
QA engineer:Fix it if need on your Pixel 6 (Pro).
PM/DM:Fix it if need on your Pixel 6 (Pro).