Ribbons are generally long, narrow strip of fabric, used especially for tying something or for decoration, so Lorde uses them in the context of being stuck to something, or being tied in something, in this context, ribbons.
"Supercut" - "These ribbons wrap me up" is a direct mention to being wrapped or tied up in something, or a romantic connection.
"Sober" - "I'm acting like I don't see, every ribbon you used to tie yourself to me" can be described as another mention to romantic connection. As thought out on Genius, "Ribbons are often considered very pretty, and used to tie up presents, so you could even say that he thought he was helping her/giving her a gift by tying himself to her and governing her every action."
(more coming soon)