Then, just like an oled has transitors along its rows and pixels for timing and signaling, so too does the CMOS have a 'rolling shutter' effect caused by the sensor having it's pixels sampled row by row, column by column, just like an oled display draws its pixels.
Here's a few sources in case you'd like to learn more, but clearly if a CMOS sensor of a given resolution is constructable, the only thing preventing its OLED counterpart is the actual organic chemistry driving the pixels, which is a large reason OLEDs are better for fine pitch displays like this than LCDs, they can be made this small.
https://isl.stanford.edu/~abbas/ee392b/lect04.pdf https://isl.stanford.edu/~abbas/ee392b/lect05.pdf
I couldn't find perfectly similar cross sections of an OLED, and the wiring will of course vary a bit, but not enough to blow past the limitations of CMOS's precision lithography process.
https://www.researchgate.net/figure/Cross-section-of-the-pix...
And to give you an idea of how far that can go, Sony has a 61MP sensor that's roughly the same physical size as these displays, but basically 5-6 times as dense with photodiode based pixels instead of oled based ones. Maybe we can't make a 61MP display that size yet, but we can clearly make a 4k one (which is about 12MP, I think...)