I don't have 20TB to test with, but I tend to agree with @Gary Reynolds last comment. It should not (ultimately) require any additional space.
I have an NTFS formatted external drive where I copied 8GB of video's to a test folder. It took about 10 minutes to copy. I used the USB drive because it is slower than my SSD. Then I did a cut+paste of that folder to another folder and it was instantaneous.
One difference could be the number of files. I only had 8 files that I moved. If you have millions of files in that 20TB, then Windows will need to update the MFT and it's going to journal updates.
https://en.wikipedia.org/wiki/USN_Journal
https://en.wikipedia.org/wiki/NTFS#Journaling
So if your drive doesn't have much free space, then it would seem to point to the fact that the NTFS file system needs to duplicate the MFT entries before it can delete the source entries. I don't think that anyone is going to be able to tell you how much space that is going to take.
You can try running defrag.exe or contig.exe to see if you can optimize the MFT.
https://learn.microsoft.com/en-us/sysinternals/downloads/contig
You may have to move subfolders one at a time if you can't free up enough space to do it in one move. Maybe a Powershell script.