Using the plex metadata editor does not embed any data into your files. Plex will never write information to your files. It stories the entered data into its database. Then if you move stuff around it maybe the equivalent of a plex dance depending on what you do which is like creating the entry again in the db from scratch.
You would need to use an external tool to embed metadata into your files but be aware using embedded metadata with plex can be swamped with problems unless you absolutely know what you are doing.
