When I time machine backup my Macbook Pro, the following error is showing. macOS Big Sur

Hi there!

If the storage in your Mac and external drive are sufficient, and the formatting is okay and compatible:

First, if you do use your external drive for both Time Machine AND use as a storage location, this is not recommended, it’s typically best to use one drive for Time Machine, and another one for storage.

If you don’t use it for both as well, I may try clearing the local snapshots:

First open your backup drive from Finder, open the “Backups.backup” folder > Name of your Mac, delete the file that shows an “in progress”

Next, disconnect the external drive and turn OFF Automatic Backup in System Preferences > Time Machine.

Open System Preferences > Security and Privacy > Privacy > Full Disk Access.

Unlock, click the “+” sign and add Terminal, which is found in Applications > Utilities. (You can also drag Terminal into this window).

When done, open Terminal from that same location in Finder.

Copy and paste this command into the Terminal window, then press Return afterwards:

sudo tmutil thinlocalsnapshots / 999999999999999 4

You May be asked for your admin password to do so, is so type it and press Return (It so the typing will be invisible, which is normal).

Next, restart, re-connect the external drive, and try a new backup.

Hope that helps!

Has there every been a Failed Installation or Reinstallation of macOS on this computer ?

From the description of the error - there might be More Than one Volume named " Macintosh HD Data " on this drive.

Suggestion is Open Disk Utilities >>> View >> View ALL Attached Drives.

If possible a Screen Shot of what is represented in DU.

Make sure the destination drive is the same format as the source drive. If there is data on it already, but plenty of free space (more than the original), you may want to use Disk Utility to format a separate partition.

HFS Extended Journaled may have difficulty backing up APFS or vice versa.

If there is less space on the destination than the original, get a larger drive that hasn't been used, and format accordingly.

Thank you for supplied the above picture.

That looks normal.

No Extra or Out of Place Volumes representing a Failed or Aborted installation.

Suggest following along with both previous posters recommendations.