"Sonic 2" begins on the Mushroom Planet glimpsed occasionally in the first movie, where Dr. Eggman is living out a solitary "Cast Away" existence (right down to drawing faces on inanimate objects). After creating a powerful signal array from mushrooms, sticks, and one of Sonic's supercharged quills, the good doctor receives a series of visitors — most significantly, Knuckles the Echidna.
The fact that Knuckles first enters the story on the Mushroom Planet is entirely appropriate, given that the locale is clearly inspired by the "Sonic & Knuckles" level Mushroom Hill Zone. Since "Sonic & Knuckles" is the first game in which the red echidna became a playable character, and since Mushroom Hill Zone is the first level of that game, the stage can easily be seen as Knuckles' debut — his Green Hill Zone, if you will. As such, it seems highly intentional that he makes his first appearance in the "Sonic" film franchise surrounded by mushrooms.
This introduction includes a couple of other nods to the video games as well. Knuckles being tricked into working for Dr. Robotnik is a common occurrence in the games, and it's the main plotline of "Sonic the Hedgehog 3," where the Knuckles first appeared as an unplayable villain. Even Eggman's little Mushroom machines could be seen as intentional references to the "Sonic & Knuckles" level, which itself featured various levers, elevators, and other gadgets made of mushrooms and vines.
