For anyone needing a ray of hope, my Macbook Pro M1 began suffering from this exact same blurry and dark monochrome screen problem just prior to the holidays. My screen very closely matched the photos that I see everyone posting, so I am positive it is the same issue. Nothing I tried could make the problem go away. I even took it to the Genius bar at the Apple store. They ran various diagnostics and replaced the firmware, but couldn't solve the problem. They said that it would cost $1,000+ to repair.
Today, I booted it up after two months of not using it to find that the problem had disappeared! I saw the little white house-shaped icon and the progress bar which I think indicates that it was trying to restore itself from hibernation. The display was sharp and full brightness. I did not do anything to the machine between the time it wasn't working and the time that it was, except for letting it sit for an extended period (approximately 2 months).
Upon first powering up, the boot process did not complete normally, but I could see a normal non-blurry mouse pointer on a black screen. I then forced a power-off by pressing and holding the power button. When I powered on, everyone came up normally. I was able to login and see my desktop in full, sharp color. I only hope that it stays this way and that the problem does not return.
The machine ran completely out of power when it was sitting for two months. It wouldn't start without plugging it in. When I powered it on using the power cord, I saw the progress bar which seems to indicate waking up from hibernation. One other thing is that the temperature in the room where the machine sat was around 50 degrees for most of the time it sat there. I doubt that matters, but perhaps.
So... my advice is to try running your machine completely out of power and let it sit for a while (maybe in a cool room just in case). I doubt that the full two months is required. You could try various periods of time to see if it helps.
To me, this result indicates that the problem isn't a display hardware failure. However, that leaves open the question of why replacing the display does solve the problem. It could be that the process of replacing it ends up triggering the same kind of reset as running it out of power and letting it sit for an extended period.
Or... maybe the problem is just intermittent and the 2 months of sitting had nothing to do with it? I'm open to theories.
I'll let you know if anything changes.
Macbook details:
16-inch Macbook Pro from 2021.
Apple M1 Max
32GB
macOS Sonoma Version 14.2
Built-in liquid retina XDR Display (3456 x 2234)
If you have any questions, let me know.