I just received a warning message from Norton 360 to fix an issue and the Norton setup screen told me to give permission again. Even after doing so, the network monitoring setup screen which shows up after system extension check screen was showing animation indefinitely:

So I had close Norton and after opening it again, I see this:
Norton's menu in the menu bar:

No matter how many times I restart Norton I see the same thing. If I click Help -> About then I can see that it has been updated to 8.6.7 already. Looks like it's a bug. I will restart my MBP and let you know if the problem persists.
My system specs:
16-inch MBP
macOS BigSur 11.5.2
Norton 360 Premium
Update: This problem went away after restarting my Mac. Looks like it's a bug and needs to be fixed as it will confuse users. Also I can see 3 com.symantec.mes.systemextension crash logs which happened few minutes ago in the console window. I have uploaded those crash files on my Google drive: https://drive.google.com/drive/folders/1Le__IzRgmRDApP56HsLm3X_FV692lrRo?usp=sharing
Also, please keep Norton 360 for macOS on par with Windows version. It's a stripped down version!!
Thanks
I had a similar problem on a MBP running Catalina after the 8.6.7 update. The Norton 360 app wouldn't open at all. A Norton popup said it needed to update a system extension, but nothing happened when I clicked to update it, probably because the Norton 360 app failed to open. I had to fully uninstall, run the RemoveNortonMacFiles cleanup tool, and reinstall Norton using the latest installer.
Before starting the new installation, make sure that you have connectivity to the Internet. Even after I properly uninstalled and ran the cleanup tool, the network on my Mac was hosed. I found a Norton 360 network interface left behind in the Network preferences. To get the network working, I removed that interface, clicked Apply, and restarted the Mac for good measure.
My system seems to be working for now, but these Norton update issues are a continued source of frustration.
New day, turned on my MBP. I received a warning that my machine was at risk and and that notification vanished automatically. Checked Norton, it looks good but when I checked the console, I can see 5 crashes of com.symantec.mes.systemextension which happened few minutes back, which was most likely the reason and looks like it's buggy as usual
. I have uploaded those crash dumps to that same Google Drive folder. Obviously, it's not because of malware, it's most likely because of that bug or a new bug introduced with this new version. Please fix your buggy software and add some more features to it to keep it on par with Windows version 
Thanks