Why you’re locked out

This isn’t a permissions problem at all – the internal SSD is completely full.
When the APFS volume that holds your home folder has no free blocks, macOS will

• pause iCloud Drive sync,
• hide anything that was still uploading, and
• make parts of ~/Library/Mobile Documents (the real iCloud Drive folder) inaccessible.

Because of that, Finder’s “Get Info”, chmod, etc. can’t help.
Your admin account already has root rights via sudo; you just have to give the system some breathing room. fix You only need a few gigabytes of free space for everything to unlock again. Stop Carbon Copy Cloner and delete its snapshot

CCC makes an APFS snapshot of the source before it starts copying; that snapshot is probably eating tens of gigabytes.

• In CCC choose Delete SafetyNet / Snapshot

• If you can’t launch CCC? Use Terminal:

  sudo tmutil listlocalsnapshots /
  sudo tmutil deletelocalsnapshots <snapshot-name>   # repeat for every name returned
  
  

Then turn iCloud Drive off

• Files that have already reached the cloud stay there.
• Anything that never finished uploading (CCC copy) is moved to
  ~/iCloud Drive (Archive)/.

Then try deleting you failed copy

This can be done in your terminal like so

sudo rm -rf ~/iCloud\ Drive\ $$Archive$$/<big_folder>
If the archive folder wasn’t created, look in
~/Library/Mobile Documents/com~apple~CloudDocs/ instead.

Turn your iCloud back on and give it a few minutes everything that was fully in iCloud reappears and your local copy should be gone