The whole point of screensavers is that they actively display something different than what the screen normally has. Burn-in is not a problem that originated with OLED, and last time anybody had that problem, screensavers were the best mitigation they came up with.
OLED burn in happens because the organic stuff used to color the light into RGB degrades at different rates for the three colors. So for OLED, having an image on the screen for 30 minutes is the same as having it on the screen for 5 minutes, 6 times.
If the Windows taskbar is present 95% of the time that the computer is being used (with the other 5% being fullscreen applications), and a screensaver is active 40% of the time the screen is on, then the taskbar is still visible for 57% of the time the screen is on.
Maybe the tech has changed, but as of my first OLED phone 7 years ago, blue (the same color as the taskbar's Windows icon) was the fastest color to burn in.
Newer phones shift the navbar and status bar items a few pixels every minute. But the start menu icon is too big for that, so after a year or two, every time the user watched a movie in fullscreen, they would get a blue blob in the lower left corner.