What technology does this State Online icon belong to in Windows File Explorer

Solution 1:

In general it is used for the "Offline Files" feature, which is a built-in part of the SMB file share client – it is able to locally cache contents of a share to some extent. Look for a "Make available offline" option in Windows Explorer's menus.

The feature has existed for ages, though received a major rework in Vista (or Win7?) together with the sync status icon.

It is used not just when accessing a remote share directly, but also when accessing a standard folder like Documents which has been relocated to a network share using "Folder Redirection". (This is defined through a Group Policy.)

"Online" means the share you're accessing is fully reachable and you're working with files directly on that server. If the network connection was lost, you'd still be able to make some changes and they'd be propagated later.

Do note that Offline Files is only a cache, and the files aren't permanently synced to a specific visible location on your computer (i.e. there is no equivalent to the ~\Dropbox or ~\OneDrive folder).

The same icon might also be used for the "Work Folders" feature, which I think is WebDAV-based access to SharePoint (never tried it).