Yes, this IS A PROBLEM. Last month under Catalina, internet access worked fine. Two weeks ago, I upgraded the MAC OS to Big Sur, and still everything worked fine. Then one day last week Parallels updated to Version 16.1.1 (49141), but I don't think Parallels Tools was updated at that time, but I did not pay that much attention to it because I thought everything was working just fine. Then, the other day I saw a new version of Parallels Tools get installed and I believe that is when the problem started. The next morning when Quicken was attempting to log on it came back with the error saying that it could not get to the internet. Strange, I just downloaded my mail on the MAC side and everything was fine. I checked Safari on the MAC side and all was good. I switched over the Windows and Internet Explorer and it could not find the internet just like Quicken. I guess I really did have a problem. Now, after FAR TO MANY hours spent on this problem, I have at least temporarily resolved the internet connection side of the problem. By going to Parallels> Configure> Hardware> Network> I saw that my network Source was Shared Network (Recommended). I switched it to EACH OF THE Bridged Network choices (Default Adapter, Wi-Fi, and Ethernet) and they connected me to the internet; however, at slower speeds than when on my MAC side. So, while this appears to be a temporary solution that allows me to connect to the internet, I do not think that the computer can actually "see" all the files on that MAC, i.e., full sharing.
I sure hope this gets enough attention of the experts at Parallels this week, because not having internet access IS A BIG DEAL for many. Let's hope for a quick resolution.