Well, mine is win 10, 21H1, OS Build 19043.1165 -- & just a week/so ago Backup & Restore (Win 7) worked fine to rescue this computer from an unbootable situation. OK, it was OS Build ...1151 at the time.
(1) Why did you reinstall Windows before attempting to restore the image? Did you want to use the new Recovery partition (Shift+Restart goes there) to do the restore? That might fail when the other partitions in the image (Windows & EFI/System Reserved) are a different size or at a different location than in the image. This is because the restore process will not reformat the drive when the Recovery partition is in use.
The restore process would reformat the HDD itself, if run from a Repair Disc, a USB Recovery drive or Installation media. Then, you would get all the partitions back exactly where they came from -- including the Recovery partition that is in the image, & it will match the version of the rest of the installation too.
(2) Do you have 3 external hard drives or just one with 3 partitions?
(3) And each partition has just a WindowsImageBackup folder in it?
(4) And none of them show up in the image restore window?
(5) Can you read & write other files to the external HDD?
(6) Can you mount any of the images...?...

(a) Open the WindowsImageBackup folder, then the computername folder & finally the "Backup..." folder.
(b) Double-click the largest .vhdx file inside the Backup folder to mount it.
That will be the image of the C: partition. It will get a letter (say, E:) & open in a 2nd instance of File Explorer. You may put it side by side with the 1st instance. Then browse to your files & copy them from E: to C:. (But I wouldn't try the reverse.) When done, right-click E:, & select "Eject".
[But I must add, the first time you double-click a .vhdx, it may give an error message. So, just OK the error, & open Disk Management. The mounted image will have the same name C: had when the image was made, but no letter. Put a letter on it, & it will show up in File Explorer.]
- This was the situation prior to creating the problem where I was not able to restore the windows 7 image file. I had a dual boot system which was created by Ubuntu when I decided to add Ubuntu and Windows was already in the system, therefore Ubuntu became the boot OS. The Windows partition was getting full and I had extra unused space in the Ubuntu partition, so I decided to extend the windows partition by using some of the space available in the Ubuntu partition, which was listed with an ext2 format only, and the repartitioning software did not allowed me to extend into it. Not knowing better I changed the Ubuntu partition type to Primary hoping that would allow me to extend into it. That was what created the problem, I could not boot after that. It would boot into some linux gnu something command. I don't know linux and I looked online for the error I was getting and there were some responses but none worked or did not have enough information about how to use the information. Anyway, after a while I got frustrated that since I had a backup only about a week old I could restore it if I reinstalled Windows, which I have done in the past. After trying different things to try to reformat and reinstall Windows I finally was able to do it, and the rest I already told it.
- I have 3 external HD of different sizes: two where only there is only one backup and one where there are 4 backups in their own partitions.
- Yes the only contents of the partitions where there is a backup is the WindowsImageBackup folder.
- No, none of them show in the Restore window, but as I explained before, this has nothing to do with what I did with the laptop with the dual boot system, since the same thing happened with the other laptops when I tried to see what happens when I used the Restore feature.
- yes, I can read and write to the external HD using File Explorer
- Even if I were able to mount and copy files, that is not what I want or need. The contents of all the installed files is over 500 Gb and I have lots of installed programs and I cannot just copy the installed program files since they would not work or run because the registry does not reflect their installation. The only solution is restoring the whole image.
By the way, the procedure to mount the vhdx file is more complex than that. Since I tried double clicking the file to mount it and it did not work, I did a search and found this procedure: How to Create and Mount VHD / VHDX File in Windows 10 – Step by Step Guide (systoolsgroup.com)