One option:
Initialize the new app data drive and make sure the docker compose files all point to the new drive. It would be useful to know how you went about mapping this, ie in the env file, or differently for each docker compose files. Ideally it would be just updating a single line. This is where I would personally start before doing anything else, identify the mechanism in place that links the containers to the data.
From there, you’ll want to gain access to the backup data. The usb drive is connected but you can’t see it via GUI? Are you able to see it via ssh? If so, the cp command can copy the backup directory fairly easily.
If you have another machine capable of mounting the backup drive, you could use it to copy the backup files to the newly initialized app data disk. it could be a simple drag and drop if the new drive is reachable via network share. You could even set this network share up just for a temporary use.
Once your backups are copied and the docker compose files are correctly pointing to the data, bringing the containers online should restore their configurations to whatever point they were backed up.
Let’s start with the first step, how do your compose files map to the app data?