after update macOs to 12.7.5 I always get Time Machine error: an error occurred while preparing the backup.

You can use Drive DX to possibly get a better view of Drive health…

https://binaryfruit.com/drivedx

For further clues if need be...

How to fix File system verify or repair f… - Apple Community

https://forums.macrumors.com/threads/does-anyone-know-how-to-fix-error-69845-in-disk-utility.2340887/

Have you run Disk Utility's Disk First Aid on all connected drives?

In Disk Utility>View, select Show all Devices, highlight the top left entry.

Run Disk First Aid on all items in the left panel, from top down.

Are you running any VPN, Anti-Virus, or Cleaning apps?

No, I don't think that is needed.

This a tough one to figure out, but...

To find out if it's system wide or user specific, try this...

Open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

Does it work in the new account?

I am having the exact same problem. It is happening on multiple computers. I did notice the Time Capsule when it mounts changed its name to “Data” instead of what I named it. It is still named my old name with I use Airport Utility. At first I thought it was the old problem where the sparse bundle is corrupted and your only option is to delete it and start over. The reason I came to that conclusion is because when I tried to set up a new time machine disk, I used Data. I then was giving the chose to Use an Existing Disk, Erase Existing Disk, or Choose a a different disk. First I chose using Existing Disk. It asked me to enter in the password for the sparsebundle since I have an encrypted backup. My password didn’t work. I then chose Erase Existing Disk. This appears to work. I am 1% done with my backup so it appears to be working. What is odd is when I look at existing Time machine back up disk, the one I supposedly just erased is still showing up. Maybe the sparsebundle was what was deleted and the old name of the disk is still there. I haven’t been able to connect to it since the update so maybe it is just a phantom drive now. My conclusion now is that the OS update changed the name of the Time capsules to whatever you named it to a generic name “Data” Please tell me if other people’s Time capsule name is now “Data”. I hope someone at Apple reads this and there is an OS update. Although, by the time an update is issued, I will have already have my new backup so they need to keep in mind to not erase “Data” so I have to do it again.

I just realized that one of my computers is brand new and it therefore running. Sonoma 14.5. I set up this computer using Time Machine but the new computer’s Time machine also doesn’t work. It is showing the backup as now called “Data”. Therefore, the flaw appears to be in multiple OS’s.

No, that is totally unrelated. I am not booting off an external drive; I am simply using Time Machine to back up to a Time Capsule. Since Time Capsule’s are no longer supported, I suspect that is what the problem is. The last updates somehow changed the name to “Data” instead of what you called your Time Capsule. It appears that I need to complete start over and create a new Time machine backup. There may be a way to change the name by going to the command line but I don’t know where it is located so I didn’t try. I guess I could have gone into the command line and tried to find where it is but I didn’t.

See if my last reply here at 12:52 PM helps explain what you're seeing...

Revert back to Main Startup Disk from Ext… - Apple Community

Did your Time Capsule name of available disk now show one called, “Data” See my comments below.

OK, it does sound like you need to start over.