The “Files” link next to the subdomain is an easy button which connects you to the htdocs folder of that specific domain. So instead of having to use the main File Manager button and then looking for the folder yourself, you just click that button and can start editing right away!
This option isn’t new though. It has been there for years, but it looks a bit different with a design update of the client area.
But in your case, it does look like all files and directories are gone, so neither button will show anything. I don’t know what happened, but it seems very unlikely that you’ll be able to restore your files. So I also think you’ll probably have to start over.