Just wanted to chime in as well I've had my 42" lg c2 evo for around 9 months now. I have pixel shifting enabled and run the refresher once a month. Haven't noticed any burn in at all. I use it for heavy gaming and media consumption primarily with some static elements in the games I play.
I do however have detection issues with mine were it will display the bios just fine even the windows logo on start up but as soon as it hits the desktop sometimes it will display no connection.
In the past I would have to unplug and re plug the hdmi cable 1 to 5 times before it would show the desktop. I tried changing out multiple high quality 8k cables including an expensive optical cable and they all produced the same effect. I did read up on the issue and found an easier way to address the problem by holding down the power button on the TV itself for 5-10 seconds until the power led flashes. That usually solves the issue in 1-2 goes. I have it connected to an rtx 4070 and I fear that it may be a hardware issue with either the TV or the graphics card.
Just take what I say with a grain of salt because it deffenitly seems like an edge case as I've only seen a handful of reports with the same issue I'm experiencing. I deffintly won't dock it hard as it's just a mild annoyance that I encounter once a day, deffintly still mad in love with this OLED.
One other weird issue I have is sometimes when I'm playing shooters some one will say the word "menu" or something similar and the mic on the remote picks it up and displays the menu on the TV. It has gotten me killed a few times already lol.