CX, yeah; the C9 stock has pretty much dried up at this point. For non-OLEDs you'll probably want to ask someone else since I own an OLED personally, but I know the Sony X900H is really popular.
I've had an LG B6 since mid 2017 and I've had no problems. I've left static UIs up for over an hour at a time with no issue, though the TV does dim after a time when it isn't being used. Even some older stuff on the Mister like NES games with the top UI always there.
Burn in is no where near the issue it was years ago. Tech in modern TV accounts for burn in and does things to avoid that. Even if you get mild burn in after leaving something static up for a long period of time, a simple screen wipe video running for a few hours usually does the job.
You really have to try hard to get burn in on your TV these days. I watch Twitch on my TCL from 2018 constantly and there should theoretically be a permanent chat box imprinted into my screen, but there's nothing. Sometimes I fall sleep with the TV on with a menu up, etc.
I think even a 2020/2019 OLED shouldn't be too bad with burn in.
