There are a handful of games coming to Switch that don't support cloud saves, and it's usually tied to cheat prevention methods. Pokemon Sword & Shield is an example, and while it's sad to not have the feature supported, at least it makes sense. Unfortunately, it seems that The Legend of Zelda: Link's Awakening is joining that handful of games, but we have no idea why.
The official UK page for Link's Awakening states that the game will not support cloud saves. There's no word as to why, and it's hard to come up with reasoning that makes sense. Hopefully this is just a mistake on the page itself. We'll reach out to Nintendo for confirmation/explanation.