How were these backups created? Time Machine, or did you use some third party backup software?
What size are these backup drives and have you used them with this specific Voyager dock before?
Are these backup drives hard drives or SSDs?
Have you tried disconnecting all external devices and have you connected the backup drive directly to the laptop? Is the laptop plugged into the charger?
Have you tried using another USB drive dock or enclosure or using a different USB Cable and adapter? Try connecting the drive to another USB-C port especially on the other side of the laptop. Also try rotating the USB-C connector on the drive cable 180 degrees upside down (I know this sounds crazy, but it can sometimes work if the USB-C port is bad).
Is your laptop booting and working correctly or is this the reason you need the backup to restore the laptop to a known good state? Or are you just trying to restore a few file instead of the whole system?
Are you booted into macOS normally when trying to access the backup? Have you tried booting into Safe Mode to access the backups?
If your laptop is able to boot normally or into Safe Mode, then you can attempt to check the health of the external drive(s) by running DriveDx. You will need to install a special USB driver so that DriveDx can access the external drive's health information. However, even with this special driver some USB drives will still block the necessary communication to access the USB drive's health information. Post the DriveDx reports here using the "Additional Text" icon which looks like a piece of paper.
Edit: I forgot to mention that Drive Savers and Ontrack are to professional data recovery services that are recommended by Apple and other OEMs plus both vendors provide free estimates. Our organization used Drive Savers several times many many years ago and we were satisfied with them.