Permission to edit media files (photo captions, alt tags)

Question

What permission is required for a user to be able to edit all media files in Wordpress?

I'm trying to edit the captions and alt tags of some media files in Wordpress. I can see the media file in the "Media" section of the WP Dashboard, but if I click on an image then the Alternative Text, Title, Caption, and Description fields are all greyed-out; I cannot edit their contents.

I can upload media. For any files that I've uploaded, I can edit the above-listed fields. It's just an issue with editing the fields of older photos that were uploaded (by other users) before my account was created.

I see that there used to be an edit_files permission in Wordpress, but the documentation merely says that it's no longer used

Edit Files

• Since 2.0
• Note: No longer used.

(source)

Unfortunately, I can't find the replacement for the edit_files permission.

What granular permission should I ask the WP administrator for that gives me only permission to edit all the media files' alt tags, descriptions, and captions -- following the principle of least privilege?