Copyright

Adobe doesn't, and can't, copyright anything that you have created - that's not how copyright works. To copyright anything, you have to claim and state that you are the legitimate owner or author of the work. You can, though, state this in the notes section of a file's metadata - but there isn't a specific section for this; it has to go into the notes.

Copyright is complex; just stating that you have it over any particular work it isn't really sufficient, and in this modern digital age, the rules about it are somewhat out of touch with reality, I'm afraid. But even with the existing system it's complex when it comes to recordings, as the maker of the recording retains a 'mechanical' copyright, even though the copyright in the work recorded may not belong to them. This is a significant reason that it's not catered for in the metadata fields as such.