Trying to infer from your post what the issue may be:
I have an empty Documents and Desktop folder in iCloud but it said that it's full (5.9gb / 5gb)
It cannot be both empty and full. Empty Desktop and Documents folders may be from turning on/off the Desktop and Documents feature without syncing data.
have two Macbooks with the same name, there are NOT two sets of folder on iCloud so I think it completely broke.
Likely not. Only Desktop and Documents would create new folders by device. If you have devices with the same name they will be indicated with (x).
So there's files there that I can't see and I can't fix it.
Any file available to you is at iCloud.com.
Doesn't help that it's impossible to contact someone re. support.
Visit get support.apple.com
I basically have no iCloud drive and my LOCAL Documents and Desktop folder contents are now wiped.
See the following instructions from Add your Desktop and Documents files to iCloud Drive - Apple Support
Turn off Desktop and Documents
When you turn off Desktop & Documents Folders, your files stay in iCloud Drive and a new Desktop and Documents folder is created on your Mac in the home folder. You can move files from iCloud Drive to your Mac as you need them, or select all of your files and drag them to the place you want to keep them.
- From your Mac, choose Apple menu > System Preferences. Click Apple ID, then click iCloud. On macOS Mojave or earlier, choose Apple menu > System Preferences, then click iCloud.
- Next to iCloud Drive, click Options.
- Deselect Desktop & Documents Folders.
- Click Done.
If you turn off iCloud Drive or sign out of iCloud, you have the option to keep a local copy of your files that are in iCloud Drive. Whether you decide to keep a local copy or not, a new Desktop and Documents folder is created in your home folder. If you choose to keep a local copy, your files in iCloud Drive are copied to a folder called iCloud Drive (Archive) in your home folder. Then you have the option to move any files that were in your iCloud Desktop and Documents, back to your new local Desktop and Documents.
Honestly, iCloud drive is the worst piece of data backup/synchronisation software I've ever used.
It doesn't even have a way for me to SEE what's stored in the 'full' drive
You can always see what is stored at iCloud.com or on any connected device
As well as not being able to customize which folders are even synced, so I have to store everything in funny places to NOT get backed up (big data / code / whatever that isn't documents)
Correct, you cannot choose which folders to sync; you do have the option of syncing desktop and documents. Anything that you wish to retain offline needs to be stored in a folder that does not sync.