Zelda plays a tiny role in this non-Hyrulian game, in which child Link - having lost Navi, his fairy companion - sets out on Epona and gets lost in Termina following the events of Ocarina of Time. And she doesn't have much to say, either, other than "THANKS LINK, YOU'RE THE HERO OF HYRULE."
Like every other NPC in the game, in the OG Legend of Zelda, the titular princess delivers her lines to Link in an ALL-CAPS SHOUT. The game that first created the Zelda/Link relationship didn't go particularly hard on their dynamic - after all, the year was 1986, and "hero saves princess" was good enough, without added layers of "also they're childhood friends" or "and one of them is REALLY sad". This doesn't change anything about Link's relationship with Naptime Zelda, it's just a fun fact. To make things extra complicated, apparently, this Zelda is a different Zelda to the one in the first game, but the Link is the same Link. Hard to have a relationship when one of you is in a coma, isn't it? Sure, the plot of underrated 2000s rom-com Just Like Heaven would beg to disagree, but in Zelda II, the plot revolves around Zelda being a sleepy gal that Link needs to wake up.