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.]