Desktop and Documents folders appeared on desktop MacBook Pro 14in M5

"After downloading files from a couple of backup disks, I suddenly have Desktop and Documents folders on my desktop. The Desktop folder contains everything that's on my desktop, including a Desktop folder! The Documents folder is the same - it contains everything. I experimented by trying to take a file from the Documents folder and put it on my desktop but nothing happened. I can't remove the folders from my desktop. If I put them in the Trash, I'll lose everything. What on earth have I done????? And how can I fix it???"

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Ridding of Transferred Files:

Well, you manually transferred these files, rather than using Migration Assistant. Is that correct?

A. If so,...

1. Create Time Machine Backup of this Mac to an external hard drive that is at least twice the capacity of what is already stored.
2. Reset this to Factory Settings, as if you were to sell it. Perform as instructed here, including the iCloud log out: What to do Before you Sell, Give Away, Trade in, or Recycle your Mac - Apple Support
3. Perform a transfer from the Time Machine Backup you just created in Step 1.
4. Transfer the rest of it from the other Time Machine Backup(s) though use of Migration Assistant.

All ought to transfer accordingly.

or...

B. If not,...

1. Create Time Machine Backup of this Mac to an external hard drive that is at least twice the capacity of what is already stored.
2. Restart: the Mac.
3. Trash: these files
4. If any issues, Restore your Mac from the Time Machine Backup you just created in Step 1.

“[…]So, I put a new folder onto the desktop and slowly transferred all the files into that new folder. It worked too. They are all sitting there safely, waiting for me to file them neatly away.[…]”

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Excellent job troubleshooting this!

"Yes. Didn't use migration assistant. Bloody heck. (Thanks for responding. Again.)"

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You are welcome.

Let us know how it ends up working out.