Actually, in Japanese Edea's name is more like "Idea". So it could have been a Connect Edea Device.

There's this strange thing that happens on disc 3. Rinoa is in a coma. Squall is able to talk to Ellone in the dream world, Ellone thinks "Oops, I must be asleep". And she basically tells Squall that she's given up trying to change the past. Meaning no more dream sequences. Right?

Except there's 1 more when you get Esther. Was this Ellone's doing? Or was it Ultimecia trying to connect to Edea (who's in their party) not realizing Edea doesn't have sorceress powers anymore.

This dream sequence tells us what happened to Adel. Potentially informing Ultimecia of Adel's whereabouts as well (if she didn't already know).