Quick answer: No, Animal Crossing: New Horizons does not have a story mode in the strictest sense. The game falls under the umbrella of the life sim genre. Most of what you buy, find, create, and do is on your own terms.
Whether you’re playing on Xbox One, PS4, or Switch, games typically fall into one of two categories – narrative based or multiplayer focused experiences. Animal Crossing: New Horizons, a game that has lit the world on fire in these off kilter times, bucks this trend. Similar to Minecraft or The Sims, Animal Crossing is absent of a well defined story mode. Instead, the crux of the game is personal expression, progression, and finding a way of (virtual) life that works for you.