"Macintosh HD - Data"

You need to forget everything you think you know about how macOS works. Starting with Catalina and Apple’s new file system called APFS the rules of game have changed dramatically. Macintosh HD - Data is a critical part of how macOS Catalina stores user data. Removing it would kill your installation and lose all of your user data. Catalina divides the boot device into two volumes, Macintosh HD and Macintosh HD - Data. Macintosh HD contains all of the operating system’s files and data. It cannot be altered at all by the user. Macintosh HD - Data contains all of your user data, files, apps, documents, etc. macOS Catalina manages both volumes separately but Finder shows only Macintosh HD. It’s all under-the-hood stuff.

And Macintosh HD - Data does NOT prevent backups to Time Machine. Millions of people have been using Time Machine with Catalina and now Big Sur with no issues at all.

You have an orphan Data volume left over from an improper reinstall.

Open Disk Utility and look for two Macintosh HD - Data volumes.

Select each and remove the one that has a Mount Point of /Volumes.

The current one will be mounted to /System/Volumes/Data.

When you eject the HD - Data that means none of your user data is being backed up, rendering Time Machine useless to you.

How is your Time Machine volume formatted? Catalina still requires Time Machine to be formatted Mac OS Extended (journaled). Big Sur now prefers Time Machine to be formatted APFS. You might try reformatting your Time Machine drive and trying a complete new backup. You should also verify that you only have one Macintosh HD - Data volume. For some reason we have seen double - Data volumes on systems that were formatted incorrectly before installing Catalina.

Did you create another Macintosh HD - Data Partition when you reinstall it?

Or Did you make a copy of Macintosh HD - Data

Select the below one (Without the home icon), then click the ‘—‘ icon.

Make sure you do not mess up with your computer systems next time

You don't. At least, not unless you want your installed third party software and your entire user account to go bye-bye.

You’e Welcome,

Try Backup your mac to test if it works

I hope you’ve deleted the correct volume

Try checking it again in Apple Logo>About this Mac>Storage

And also check back on Disk Utility, Check on Macintosh HD - Data and send a screenshot both of it

The one that has least info is a copy

How to check?

1. in the Apple logo, click About this Mac
2. Click on Storage
3. Screenshot it and send it here

choose this one below

then, click the ‘—‘ icon

If you cannot remove the volume because it’s in use:

1. Boot into macOS Recovery on Intel-based Mac computers or if using M1 chip, Use macOS Recovery on a Mac with Apple silicon
2. Open Disk Utility and Try again the steps above.
3. if you’re done, Restart your mac

Well, you're wrong about that. I keep getting a message from Time Machine saying "Time Machine couldn't compolete the bakup to "LRC-web". Time Machine could not back up the disk "Macintosh HD - Data" because it is nearly full. Delete some files on this disk and try again. "

My disk is not about full. When I go to About this Mac>Storage, I see "Macintosh HD 646.14 GB available of 1.12 TB. My Time Machine drive also has 1.29 TB available of 4 TB.

It seems to me this is your system screwing itself up. What should I do?

Next time screenshot the full window of Disk Utility

The one with the home icon is the in-use data volume.

They’re both from macOS. One is just from another macOS. it wasn’t removed prior to the reinstall of macOS