Hi,
Please run "winver" command to check your system version.
"Checked different things found like System Volume Information directory not having the good permissions, the $RECYCLE.BIN folder also"
It is an expect behavior, Windows will use this folder for certain system-level features. The permissions are set to prevent users—and programs without the appropriate permissions—from tampering with the files inside and interfering with important system functions.
For more information, we could refer to: What Is the “System Volume Information” Folder, and Can I Delete It?
I noticed you checked with 2 third party software tools and show F drive as 5 GB. Did you checked if any changes on that size just using File Explorer to assessment it? We also could open F drive in file explorer and choose all folders to get totally size after right click it. (You should show unhidden files at first.) As I know third party software is not available to check file size which it have not right to access. To avoid this, I recommend to check some big files' size which also have not right to access separately in file explorer. A capture would be useful to get a clear understanding for it.
By the way, as I know, if you have file name longer than 260 characters, it will cause calculate issue in file explorer. So please check file name size on your side.
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Bests,
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