I would like to say how it is a fine honor for Knuckles' Chaotix to be chosen as this month's "Maps of the Month", but the story from the Western Manual is a bit contradictory to the actual story read from the Japanese Manual, if I'm not proven wrong, for there's no actual mention of Carnival Island or said Power Emerald as the focus of the game.
The actual exposition is this...(I'm giving this story my 2 cents based on the JP manual and my own perspective of its events, so I hope I'm right on many things)
Dr. Robotnik(or rather, Eggman) had discovered a mysterious island that rose from the ocean, the south sea, precisely, after his defeat and Mecha Sonic Mk.II's defeat in "Sonic the Hedgehog 3"(both halves, to be precise, including Part Two, still called "Sonic & Knuckles"), and travels there to find an intriguing legend centering on the Chaos Rings, ancient rings infused with the Chaos Emeralds' power from long ago.
Through his studies, Robotnik was able to discover the Chaos Rings' secrets to harness their power. Moreover, their prime use is to summon the Master Emerald, Angel Island's power that keeps it afloat, at will, anywhere, by the user's command. With that power, he could once more easily attempt to conquer the world, so he built his own resort/fortress called Newtrogic High Zone, and all its alleged "attractions" the game has as its Zones.
A little later, a small group of wanderers, Vector, Charmy and Espio, haven't yet formed the Chaotix team, had gathered upon hearing disquieting activity going on in the island and pitched their own 2 cents on the island's legends, with Mighty, having been without Ray since SegaSonic's events, joins in on the expedition, upon faintly hearing a familiar adversary at work there.
Once there, they all find Robotnik's already searching for the Chaos Rings, but despite them doing well for a bit, disputes had accidentally triggered its security systems, alerting the new batch of Badniks to their presence. Tried as they might, they all ended up captured by Metal Sonic, repaired since Sonic CD's events, and were confined to the Combi Catcher.
In the midst, though, two Badniks, Heavy and Bomb, having been made from an accident during production, quietly escaped the facility and sought to figure out how to leave the island.
Later, Knuckles, having returned to guarding the Master Emerald, felt a concerning tremor, and as if by coincidence, a glow of alarm shined on the emerald, showcasing what Knuckles saw on the island. The visions saw Robotnik trying to discover the Chaos Rings and feared he would actually use them to rule the planet.
Before leaving, though, the Master Emerald was able to show him an inscription showcasing a necessary ritual that can actually destroy the Chaos Rings before anyone can use it in the wrong hands.
With the knowledge in hand, Knuckles sets off on his own adventure to save the world and make new friends along the way, leading to the actual adventure.
That's what I would think of it, anyway. Hope I'm correct.
Also, greetings on the forums!