Despite a plethora of contradicting reports online, I can categorically confirm that an OLED panel can suffer screen burn or image retention.
Because the 4000t/5000t units have no “screensaver” facility when paused, I now have a lovely ghost image of both the volume triangle and the big blue play button.
My LG ec930v has screen dimming that kicks in after a while but obviously this has not been enough to prevent the issue. My model does a pixel refresh while the TV is in standby (not fully off) but it is unable to clear this up.
With newer models, I believe that you can run this refresh directly from the settings. If newer models have a proper screensaver option, I suggest that you set this up.
This has only become apparent since I moved in to care for my old Dad and I was frequently pausing either live TV or recordings if he needed anything.