My OS update was BigSur 11.0 to 11.1
Here is the disk layout from Terminal App
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *500.3 GB disk0
1: EFI EFI 314.6 MB disk0s1
2: Apple_APFS Container disk1 500.0 GB disk0s2
/dev/disk1 (synthesized):
#: TYPE NAME SIZE IDENTIFIER
0: APFS Container Scheme - +500.0 GB disk1
Physical Store disk0s2
1: APFS Volume Macintosh HD - Data 145.8 GB disk1s1
2: APFS Volume Preboot 348.2 MB disk1s2
3: APFS Volume Recovery 1.1 GB disk1s3
4: APFS Volume VM 20.5 KB disk1s4
5: APFS Volume LLLL 15.0 GB disk1s5
6: APFS Snapshot com.apple.os.update-... 15.0 GB disk1s5s1
Your Volume <APFS Volume LLLL 15.0 GB disk1s5> appears to be your Macintosh HD. I would not delete that.
ref: About the read-only system volume in macOS Catalina - Apple ...
Yours It is not a pristine presentation however it looks correct.
For a comparative reference only, a more pristine look:
MacBook-Pro ~ % diskutil list internal
/dev/disk0 (internal, physical):
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *1.0 TB disk0
1: EFI EFI 314.6 MB disk0s1
2: Apple_APFS Container disk1 1.0 TB disk0s2
/dev/disk1 (synthesized):
#: TYPE NAME SIZE IDENTIFIER
0: APFS Container Scheme - +1.0 TB disk1
Physical Store disk0s2
1: APFS Volume Macintosh HD 14.9 GB disk1s1
2: APFS Snapshot com.apple.os.update-... 14.9 GB disk1s1s1
3: APFS Volume Macintosh HD - Data 279.7 GB disk1s2
4: APFS Volume Preboot 281.5 MB disk1s3
5: APFS Volume Recovery 655.5 MB disk1s4
6: APFS Volume VM 1.1 GB disk1s5
I may have lost the thread but if you are continuing to having issues— to wipe the slate and start anew,
from Internet Recovery: https://support.apple.com/en-us/HT204904
Disk Utility>View>Show All Device it is here you select the parent Drive (not the Container level or Volume level.)
you erase/format/initialize the parent Drive and reinstall the macOS, and restore your user date from a backup.
Restore your Mac from a backup
The new drive icon, LLLL, is in a new location on my desk top each time I open my computer.
If this is your only issue, you do not have to show the Macintosh HD on the Desktop— it really is just a carry over from the old days. Make a change from Finder>Preferences>General> remove the Hard Disk selection