Time Machine Issue

Disk Utility is virtually useless with a Time Capsule. it can display the sparsebundle file......."Time Machine Backups" in your case......but it cannot display the actual hard drive......."Data" in your case, so Disk Utility is not going to tell us anything really useful about the actual hard drive on the Time Capsule.

In other words, since Disk Utility cannot display any information about "Data", it cannot run diagnostics like First Aid on "Data" to see if there might be a physical problem with the Time Capsule hard drive. Disk Utility also cannot erase or format "Data".

Here is what is happening when you try to run a backup:

Your Mac's hard drive.....running Big Sur......is formatted in APFS

The Time Capsule hard drive....."Data"......is formatted in Mac OS Extended (Journaled)

Time Machine tries to create a sparsebundle file (which is formatted in APFS) on "Data" (which is formatted in Mac OS Extended (Journaled). It's complicated.

Things were much simpler when the hard drive in your Mac and the hard drive in the Time Capsule were formatted the same.

A guess would be that the sparsebundle file......"Time Machine Backups"......was not created correctly, because of the added complications with disk formats on the Mac and the Time Capsule so backups cannot run.

My suggestion would be to open up "Data" and manually delete "Time Machine Backups", then try to run a new backup again. Time Machine will try to create a new sparsebundle file on the Time Capsule when this occurs.

I don't know if this will solve the issue, because I have not experienced the issue that you are describing.

Now, if you are saying that you can still open up Time Machine and see older backups for the Mac........while you are being told that there are no backups on the Time Capsule for your Mac.......then I'm still confused. Can't explain that one.

Please power off the Time Capsule

Power off the Mac that is working correctly with Time Machine

Restart the Mac that is having difficulty

Power up the Time Capsule and let it run for a minute or two

If you open AirPort Utility on your Mac.......(Finder > Applications > Utilities > AirPort Utility)......does the Time Capsule appear?

If no, post back to let us know that it does not appear

If yes, click on the Time Capsule in AirPort Utility and then click Edit in the smaller window that appears

Click on the Disks tab at the top of the next window

Does the Time Capsule disk......named "Data" unless you have changed the name of the disk.......appear?

At this point, you can restart the Mac that was not having problems.

Many a slip betwixt the cup and the lip with Big Sur..

Especially with old tech device like a Time Capsule.

Mount the TC in Finder on the computer having issues.. if it refuses to mount.. use Go, Connect to Server in Finder and put in

smb://TCnetworkname which should then be followed by asking you for username and password.

Alternatively use smb://10.0.1.1 or whatever IP address the TC has. Get the IP from airport utility on whichever Mac it works from.

Tell me if you cannot get the TC disk to mount.

Once mounted in Finder it is usually no problem to select it in Time Machine preferences. Tell me if you have trouble with this step.

It will also be helpful to know the network setup. Is the TC main router or bridged?

How does each Mac connect to the network and the TC?

If the TC is bridged and you connect to the main router wifi a lot can go wrong.

Plus it can be very flakey .. working one day and not the next. Reboots often help for brief periods but there is more to do to fix things if the network has gotten complicated with non-apple main router.

The TC presents itself as waiting for the initial/first backup when trying to start a backup. It starts with Looking for Backup disk, then Preparing Backup, then Stopping.

Let's take things a step at a time.

The TC presents itself as waiting for the initial/first backup

Confusing......since this would not be true if you can access previous backups, since that tells you that Time Machine has backed up previously for this Mac and you mentioned that you can see and access previous backups.

The Time Machine software stopped being able to locate the disk

Confusing again.....since you told us that Time Machine can access previous backups and it goes into a "Preparing" mode. This would not be possible if it could not find the disk.

If Time Machine can find the disk......it can, according to your information.....and it starts "Preparing".....and then stops, this is almost always an indication that your backup file on the Time Capsule has become corrupted. When this occurs, you can access "old" backups, but new backups will not run. That seems to be what you are telling us here.

To take a look at the integrity of the current backup file to check for corruption.......

Hold down the option key on your Mac while you click on the Time Machine "clock" icon at the top of the Mac's screen

Click on Verify Backups

You can watch the status of the integrity check by clicking on the Time Machine "clock" icon at the top of the screen and then clicking on Open Time Machine Preferences. This display will look similar to a normal backup, but you will see that a Verification process is underway.

The Verify Backups process might take anywhere from a few minutes to more than an hour depending on how much data is stored in the backup file. Let the process run until it completes.....or.....until you see an error message.

Please post back when you see that the process has completed. If an error message appears, please post back with the exact text of the message.