Big Sur - wakes up in sleep mode with really loud fans

Try this: Reset NVRAM or PRAM on your Mac - Apple Support

I have something almost identical. 13" MBPr late 2013. I close all programs then either just close the cover or do Apple > Sleep then close the cover. Then, either put it on the charger or sometimes not. When I open the cover, on battery or AC, I get an error message that it had to shut down and restart and I have to login with my password, or I just get my desktop screen but with no icons and with or without a spinning beachball. I don't think there has been one time yet when I open the cover and just get back to a normal home screen.

Big Sur was installed 2 days ago. I guess they have more work to do getting the bugs out. Other upgrades, minor and major, have had no problems.

Yes, reset both NVRAM and SMC and uninstalled Webroot (AV program) that I'm not sure was that compatible to begin with. I still, maybe a third of the time, get the beachball in the middle of doing something for about a minute then the screen goes black then the desktop comes back up but without the icons. I then have to restart.

Also, sometimes when I finish my session, I'll close all programs and just close the lid to put it to sleep then on the charger. Maybe hours later I'll open the lid to find my login screen, instead of the desktop, and then a message that it had to restart on its own while the it was supposedly in sleep. I've been sending more incident "reports to Apple" in the last few days then in all the last 7 years I've had this MBPr. :)

Have you tried resetting the NVRAM? Try it 2 - 3 times consecutively.

Have you run any "cleaning", "optimizing", "speed-up" or anti-virus apps on your Mac?