I am pretty sure that the Steam Deck OLED, like the Switch OLED, does not come with the pixel shifting and logo dimming features that you typically find on OLED TVs so they absolutely would be more prone to burn in. My Steam Deck OLED does dim the screen after a specified amount of time but what irks me is that the handheld still cannot download games in standby mode and instead needs to be left on while the game downloads.
I mean you could play a game while you're waiting but the hardware isn't really suited to background downloads and it would likely affect the performance in the game you're playing. Every time I turn my Steam Deck on, Steam has to down 70+ updates, mostly shader pre-cache files, for the games I have installed on the 1 TB SSD and the 1 TB microSD card and with game updates too, I can often be waiting 30 minutes or more before I can play the game. Although the screen dims, it does not go off completely - it just gradually gets darker and darker - so it does worry me that the interface text and layout may eventually burn in to the screen.