Drive wiped clean and I have a backup of that drive. How to recover everything?

If you had saved your personal actions with the Action panel contextual menu/Save Actions...  they should be here: Local drive(C)/Users/UserName/AppData/Roaming/Adobe/Adobe Photoshop/Presets/Actions (default location) or at your chosen location. . Just  use "load actions... in the Action panel contextual menu.
If you have made a backup of the file "Actions Palette.psp" you should be able to recover your action by replacing the default  "Actions Palette.psp" in Adobe Photoshop settings folder : 
Local drive(C)/Users/UserName/AppData/Roaming/Adobe/Adobe Photoshop/Photoshop settings 
If you didn't save your actions manually in photoshop or made a backup of "Actions Palette.psp" I don't think you can recover them. Sadly when you re-install Photoshop the process overwrite the "Actions Palette.psp" file... Hopefully I'm not right.
You can watch this video it's really well explained
https://www.youtube.com/watch?v=ekLZFsTYC38

If the backup software you used doesn’t have the ability to restore files to the same paths that they were backed up from, you can use the very helpful document below. It lists the folder paths where Photoshop stores settings files for many of its features, including actions, workspaces, brushes, and more:

Preference file functions, names, locations | Photoshop

It lists the macOS locations first, so scroll down that page for the list of settings locations in Windows. Use the document to find the settings you want in the backup, and copy it to the same folder path in your restored computer.