How to delete shadow volumes after install

This does not look right.

The top level APPLE SSD SD0128.. > Container disk 1 should have only two volumes:

• Macintosh HD
• Macintosh HD - Data

Please do the following command in Terminal and post the results. It will provide a much more detailed look at your disks & volumes:

diskutil list

Here's what I think you have ....

• Volume "Caution ..." appears to be what would otherwise be called Macintosh HD because it's your startup disk
• Volume "Monterey ..." appears to be what would otherwise be called Macintosh HD - Data. As the data volume, it may have been preserved when you reinstalled Catalina but at this point there's no way to know for sure.
• The two Volumes "disk1s5 ..." & "Update" are what you originally called "shadow volumes" and are still unknown as to how they were created or what they represent

If this is correct, the two volumes "Caution ..." and "Monterey ..." would be combined behind the scenes by macOS and would appear on your desktop as a single "drive" called "Caution ..." ---Is that what you see on your desktop?

I think we need more information. Please go back to Disk Utility, select View > Show All Devices and take a new screenshot especially of the left pane so we can see the entire situation with your drives & volumes.

First, for reference, this is what a normal Catalina install looks like like. There would be 5 volumes as shown below under /dev/disk1 (synthesized) - Macintosh HD, Macintosh HD-Data, Preboot, Recovery and VM. Disregard the Apple_HFS partition disk0s3 named My_iMac_Data - it's unique to my iMac.)

Last login: Mon Jan 16 20:05:01 on ttys000
martinr@Martins-iMac ~ % diskutil list
/dev/disk0 (internal, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *1.0 TB     disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                 Apple_APFS Container disk1         250.3 GB   disk0s2
   3:                  Apple_HFS My_iMac_Data            749.6 GB   disk0s3

/dev/disk1 (synthesized):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      APFS Container Scheme -                      +250.3 GB   disk1
                                 Physical Store disk0s2
   1:                APFS Volume Macintosh HD - Data     159.5 GB   disk1s1
   2:                APFS Volume Preboot                 84.6 MB    disk1s2
   3:                APFS Volume Recovery                528.9 MB   disk1s3
   4:                APFS Volume VM                      17.2 GB    disk1s4
   5:                APFS Volume Macintosh HD            11.3 GB    disk1s5

Your installation is quite different. You have 7 volumes in your APFS Container, not 5. Two volumes have unfortunate names, one has no name and there is a volume called Update. Can you help identify what each of these volumes actually is -

Monterey *****

Caution *****

Update

Blank (your disk1s5)

Second, what backup(s) do you have of your data? You seem to have a TM backup - is that on an external drive and what is its source (original Catalina install, your 'disastrous' Monterey install, or your current Catalina reinstall?) Do you have any other data backup(s)?

Third, is your MacBookPro currently functional (booting into Cataina) and exactly what model is it?

I'm sorry - I don't see any volume called "backup" in any of your posts. What is the backup volume you are referring to? And is the "Caution ..." volume the one you normally see on the desktop? Please be very specific.

I cannot explain why you have only 10GB space available. Putting aside the volume names showing in your diskutil listing, the sizes pretty much add up to to your 121.3GB drive.

If it were me, I would make sure I had a good backup of my data on an external drive. (User data only.) Two good backups on different drives would be better. And neither of them TM backups. I would then boot into Recovery Mode, wipe & reformat the SSD using the copy of Disk Utility in Recovery Mode; and then reinstall Catalina from scratch. After completing installation, I would run diskutil list to verify that I had a clean Catalina installation with no unusual volumes.

That will of course necessitate reinstalling your apps and then copying your data files back to the SSD.

Regarding "not having a 2 volume setup with Mojave." Mojave was an early (only the second) iteration of APFS and yes, it "only" had a volume called Macintosh HD that was visible. Preboot, Recovery & VM were still there but were hidden. There was no separate Macintosh HD -Data volume.

Catalina introduced the 2-volume arrangement where the boot volume - Macintosh HD - became a read-only system volume. Macintosh HD - Data was introduced as the writeable volume that contains all user home folders, user installed apps and user data. As I said before, those 2 volumes are linked behind the scenes and presented as a single "disk" to the user.