So what I am basically trying to do, is to have the ability to add custom field(e.g. Secondary URL) to Content item Meta Tab, so that the user can set it manually on demand. Reading docs did not bring any result On the attached screenshot, you can see Path, Navigation title fields, so I need to add additional one
to be able to modify the content type - in your case adding a new field - it is required to have the proper permissions via assigned roles. More specifically, you need to have permission to modify content.
Content modeling could be done via UI - see Content modeling tutorial, in your case it is Adding an element into a content group "Metadata". You also can use REST Management API for that.