I have had issues as well, especially since 11.2.1 came forth. I have a 27" LG 4K Display coupled to a 2020 16" MacBook Pro with 32GB of RAM + 8GB of AMD Radeon Pro 5500M graphics that was custom-ordered with the machine. Each were bought last year, and I had no problems with either at that time. However, since 11.2.1 came out, whenever the Display was hooked into the Mac, both the Mac's screen and the LG screen would begin a bad case of screen flickering, then go black and green almost immediately, rendering the usability of the LG Display as useless within minutes. It also would force the laptop to either perform a hard shut down, or it would restart itself. I've tried every cable that I have (all of which are brand new), with no success. I've also reset the PRAM and SMC, along with the other myriad of "solutions" that are out here (such as restarting the computer, perform Disk Utility (everything checked out OK in there), changing the cursor size in the Accessibility area of System Preferences, adjusting resolution to 1080p instead of 4K, even getting rid of the CleanMyMac X Program, as I found out that the Mac already does all those tasks in the background for you; unplugging the power source of the monitor, then plugging it in after about 10-15 seconds, AFTER the screen flickering occurs, and STILL no success. However, when the monitor is NOT hooked up to the Mac, the laptop functions normally, with no issues (which is how I'm writing this post right now). Also, Sidecar for the iPad Pro works with no issues, even when I use the iPad as a secondary display, both wirelessly and connected directly to the Mac. Also, the LG monitor is currently hooked up to the iPad Pro, mirroring its screen, with no issues whatsoever....
Another interesting tidbit: I attempted to connect the Mac via AirPlay (wirelessly) to the Apple TV, and after a few seconds of activity, the Mac automatically performed a hard shut down of itself, with the fans cutting on at a high rate for about a second before the shutdown occurred....
It seems like this issue is especially prevalent at higher resolutions than 1080p, as I did change the Display settings to "Default for Display" on the 4K monitor itself, but the issue is still present, although this flickering didn't happen until a mere 30 minutes or so later, which is still unacceptable.... I feel like it's something in the code of 11.1 or 11.2 that is blocking the ability of the AMD Radeon Pro 5500M chip and the Mac from communicating with each other, as I didn't have this problem at all when on Catalina, or even on 11.0.1.
I will admit: Even on Catalina, I'd be looking at the display, and for whatever reason, only the 4K Display would just go black for about a second, then come back on, and this would happen about every 30 minutes or so (still don't know why that was the case to this day)..... As the updates progressed, this issue of the screen going black became more common, especially while using Big Sur. I'm honestly thinking about downgrading back to either 11.0.1 or even Catalina just so I can at least continue to get usage out of my monitor, which definitely is of help to my overall workflow on the Mac.....
Question: Is anyone else out here having these same issues??? If so, please say something!!! The more attention, the better, and the more that Apple will turn its HUGE EYE (Lord of the Rings speak; LOL) towards this problem of getting these displays to work correctly in Big Sur. Besides, this is ABSOLUTELY UNACCEPTABLE, given the fact that there are a LOT of us out here that have spent thousands of dollars of hard-earned money on these machines, only to not be able to connect a display to them for presentation or professional purposes. This should be a number one priority of Apple to make sure that these basic functions "simply work" with no issues....