but the message when I clicked Time Machine on the menu bar still said last backup was September 21.
Got that.
However, when I entered TM today I found a few backups from yesterday, but nothing for any date prior to yesterday.
Time Machine started all over again with new complete backup. The old backups on the Time Capsule are corrupted and no longer usable.
Right now it is "preparing backup", but again the process is running long, may be in a loop.
There are no "loops" in the process. It either completes, or it doesn't.
Is the TC toast or could this be a software issue?
If the TC were toast, the most recent backups could not have occurred.
As it stands now, you still have "old" backups on the Time Capsule hard drive........which are no longer useable........and "new" backups which started all over again in the last day or two.
You can let the new backups continue, but you won't be able to go back and access any of the "old" backups that are still on the Time Capsule hard drive. It might be possible to delete the "old" backup file to free up more space on the Time Capsule, but this is not always an easy thing to accomplish, especially if your Mac is running the Catalina operating system.
It is much easier and faster to simply erase the Time Capsule hard drive using AirPort Utility and then start over again with a new backup. The downside to doing this is that it will take a long time for the first backup.
Not sure which way that you want to go.
It might be another discussion, but Time Machine software is frankly no longer a reliable way to back up your Mac(s). You could continue to use the Time Capsule if you want, but it would be a good idea to also back up to a USB hard drive that is connected directly to your Mac. Use the Time Capsule for Time Machine and another backup application like Carbon Copy Cloner to back up to the USB drive.