I am having the exact same issue on my 2060 Super SC Ultra, battle.net also has to be restarted after the driver crashes and recovers. I get the issue when videos or gifs autoplay on Reddit or Twitter (tested on Microsoft Edge and Google Chrome), or when content has to load on the Windows 10 Mail app, however it doesn't always happen, it's very random.
I did actually send it in for RMA but I quickly returned it to myself after I tested on my EVGA 970 and had the exact same issue, followed by some blue screen of death caused by nvlddmkm.sys as well, because I didn't want to replace a new card that I bought recently (around August), and the bsod issue occurring on my EVGA GTX 970 was enough to tell me that the 2060 Super wasn't the issue.
My configuration is i7-4790k, 16gb ram, Windows 10 20H2 and I'm using driver version 456.71. But this issue previousl yoccured on much older drivers, and older versions of windows 10 such as 1903 and 1909 and 2004.
Unfortunately I don't really have a solution, but I have been troubleshooting this for the last few months as the issue is very inconsistent and occurs randomly so it's very difficult to reproduce for me personally.
Things I've previously tried are reformatting my pc and reinstalling Windows 10, and using Display Driver Uninstaller.
It never happened on my 970 before either, until I upgraded to 2060 Super, just like how you didn't have the issue before. But unfortunately I did start to get the issue on my 970 after swapping it back to test.
It has to be a software or driver issue though...
On nvidia's game ready driver community thread regarding the latest driver, it appears to be an acknowledged issue, you can see this in the stickied post
GeForce 457.30 Game Ready Driver Feedback Thread (Released 11/9/20) Some users may experience random TDR while using a web browser 
It seems like this has to be related to our problem. I know it's a report for the newest driver, but there's no reason it can't be related to older drivers since I was having precisely the same issue.