Big Sur update -> "object map is invalid"

On Thursday evening I tried to update my well functioning iMac Catalina 10.15.7 to Big Sur. It failed, I thought because of the Apple server problems. When it failed again on Friday and Saturday, I looked more closely. Using Disk Utility in the recovery system, I can see two partitions, Macintosh HD and Macintosh HD - Data (the classic configuration). Running First Aid on the latter reveals no problems. However, running First Aid on Macintosh HD produces the message "object map is invalid" and a recommendation to backup the contents and reformat the partition.

Running df -gH in Terminal shows that Macintosh HD has used 15G. I tried to create a backup of /Volumes/Macintosh HD with tar, which reached a size of over 56G before failing. I specified that the backup file should be created on /Volumes/Macintosh HD - Data.

Even without looking at the contents of the tar-ball it is obvious that the backup included are than just /Volumes/Macintosh HD, and - indeed - navigating down from /Volumes/Macintosh HD with cd takes you seamlessly onto /Volumes/Macintosh HD - Data. There are no apparent soft links, and I thought hard links didn't work across partition boundaries. Whatever.

So, question 1: how do I create a backup of only Macintosh HD?

And question 2: do I even need to? If I am trying to replace Catalina with Big Sur, can't I just use Disk Utility to erase Macintosh HD and leave it to the installer to set it up again?

Steve