Is there a way to create a nested tag without dragging and dropping? Such as typing “root/nest” for example."
No, this is not possible.
However, here’s a little secret: It’s easily done in an AppleScript with that construct.
Here is a simple example…
tell application id "DNtp" --activate -- Uncomment this when testing in Script Editor set newTags to (display name editor) set r to create location ("/Tags/" & newTags) in current database end tell