Time Machine

HSKang wrote:

In Disk Utility, I see two Macintosh HD - Data.

Should I erase the second one?

Is this what you want?

Yes, you can try and remove/delete the "Macintosh HD - Data" volume, that has no data (813.5 KB):

The APFS filesystem, came with a new concept: the APFS container. All APFS volumes reside within a container, and the container resides within the disk's partitioning scheme. All volumes within a container share the space that is available to the container; separate APFS containers do not share space with each other.

*You can see this more clearly from Disk Utility>View>Show All Devices

ref: Add, delete, or erase APFS volumes in Disk Utility on Mac ...

About the read-only system volume in macOS Catalina - https://support.apple.com/en-us/HT210650

please report back your success or failure.

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HSKang wrote:

I just restored my Mac to a factory setting and ran Time Machine.

I encounter the error message below.

Do you want to restore your user data?

This would be to the Macintosh HD - DATA

About the read-only system volume in macOS Catalina - Apple ...

or you want to run a Time Machine back on your brand new install of Catalina??

please advise

Maybe this TM software is confused—

Lets see the output from the Terminal.app to get a better look at your configuration, from the command line copy and paste:

diskutil list internal

Terminal User Guide for Mac - Apple Support

and post your results here.

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HSKang wrote:

At the start of the reinstallation, I just erased Macintosh HD - Data in Disk Utility.

Now, I realize I have to delete it by clicking "-" in the toolbar.

Now, Time Machine is running.

And the terminal result is attached.

Thank you very much for your help.

Good computing HSKang ! thanks for your report.