LED/LCD monitors don’t need pixel washing. Sleep mode doesn’t do it. OLEDs can benefit from built-in pixel refresh cycles, but they run automatically—you don’t need to trigger them unless you see stubborn image retention. Normal gaming, even long sessions , is fine as long as the screen isn’t showing the same static UI forever.

what monitor/tv are you talking about?
brand/model

lcd with led backlighting do not burn

only oled displays burn
'pixel wash' or pixel refresh, burn the inverse image so it is all evenly burned
or image shifting burns surrounding pixels to help level out burned spots
they are all forms of mitigation, and it will have visible burn eventually
likely after a year or two of use

Even modern 2nd, 3rd gen or later OLED types generally do not those old burn in issues. As many bave been tested for 10K+ hours and saw no signs of this issue. But not every panel is perfect or will last as long before potential problems start, but that goes without saying for any type of screen panel.

LCD/LED definitely do not have tbat burn in issue. The main issues with many of those is how dull the colors can be along with low NITS brightness. And also the backlight bleeding which can potentially get worse over time. Doing 4K RGB cycle videos does not solve or help prevent those issues as people tried to claim years ago.