First let me describe my setup. I have two 2019 MacBook Pros. One iMac Pro, and two iMac Retinas. I retain the iMacs on Mojave because I run Adobe CS6 including photoshop on them, fully licensed version, and I'd lose that and have to go to a perpetual payment for a cloud based photoshop, dreamweaver, etc. if I upgraded the OSX on those iMacs.
This is my Time Capsule setup:
The Internet is the cable modem, connected with ethernet cable of course to the Time Capsule at the top that is sitting right next to the cable modem. That time capsule broadcasts WiFi to the Kitchen, Upstairs and the lower right TC, which are extending the WiFi network. The Time Capsule on the lower left is bridged and ethernet hard wired with a 300' underground Cat6 cable to a second house on the property, which is set to broadcast its own WiFi network for that house.
Each Apple computer is set to backup to a different hard drive or Time Capsule. One hard drive is connected directly to the iMac Pro with USB C for its backup, and another hard drive is connected to the main Time Capsule on the top with USB-B, for a different iMac, and then the Time Capsule that is 300 feet away from the other one, is used for backup of a different MBP and one iMac retina.
The MacBook Pro that I upgraded to Big Sur is set to backup to the main Time Capsule directly connected to the Internet, the one connected at the top. It is the only computer using its hard drive for backup, and it is now on Big Sur.
After I upgraded the one MBP to Big Sur, I did notice after about a week that that MBP was no longer backing up to its Time Capsule. It kept giving a message to the effect of that it could not find the Time Capsule. I first tried deleting the two "Time Capsule" keys from KeyChain Access - no effect. Then I hard restarted all of the Time Capsules and Airport Extremes.
Now, after hard restart, the Time Capsule would show up for the MBP on Big Sur, but I could not get that MBP to do much more than end up in "Waiting to complete first backup" mode as far as the TC, and experienced another odd issue, which was that whenever the MBP went into "Preparing to backup" mode, before it got stuck in "Waiting to complete first backup" mode, it would briefly knock the Time Capsule off the network - make it go offline and not show Green in the Airport Utility screen, and internet would go dead across the network.
As well, another odd thing that would happen, is that when that main Time Capsule came back online, the order of connectivity of the Time Capsules and Airport Extremes would change, with the Upstairs and Kitchen Airport Extremes now running off the second Time Capsule that was hard wired 300 feet away. I think this had to do with that when the main Time Capsule went offline, the Airport Extremes latched onto what was still broadcasting WiFi, even though it was far away. None of this was good.
Finally, I went into that main Time Capsule and using Airport Utility, I erased the entire Time Capsule hard drive with the second type of erase - 0 all data - and then when that was finally done, I examined the Time Capsule's drive with Disk Utility and noticed that now it is formatted as APFS.
Gradually, slowly, now the MBP on Big Sur is completing its first encrypted backup to the Time Capsule I erased. It remains to be seen if, in the future, that every time the MBP connects to that Time Capsule if it is going to push it offline as far as its functioning as a router for internet connectivity.
Has anyone else experienced this issue with a TIME CAPSULE - that once whatever device you have connected to it is upgraded to Big Sur, that every time it is "Preparing for Backup" that it knocks the Time Capsule out as far as functioning as a router for internet, for a bit?