True story: my original OP concept was devoting like a paragraph to the actual game, and spending the rest of the time talking about Chao raising. But summing up SA2 in about 5 lines or so is really hard
Eggman's grandfather Gerald Robotnik created a Sonic-lookalike called Shadow on a space colony called ARK in an attempt to create a cure for this awful disease his granddaughter Maria Robotnik has but the military double-crossed him at the last minute, killed his granddaughter and locked away both Gerald and Shadow, eventually killing Gerald but not before he could brainwash Shadow and install a death ray into the space colony in question in an attempt to destroy the entire planet in retaliation but also had a mode where the ARK's orbit would decay and smash into the planet in
another attempt to destroy the entire planet in retaliation.
Eggman learns about Shadow but pretty much none of the other shit from the previous sentence and so breaks into a high-security military base to break out Shadow, leading the colorblind military to arrest Sonic despite the hedgehog having saved the planet several times over because he happens to look like the escaped prisoner, which gets Tails and Amy involved as they go about rescuing Sonic from the military.
Dr. Eggman meanwhile learns about the cannon his grandpa made from Shadow, who's hiding the whole "I'm going to kill everyone on the Earth to avenge Maria" thing that Gerald implanted in his head from everyone, and goes on a quest to grab all the chaos emeralds which scattered since the end of the first
Sonic Adventure, accompanied by Shadow and newcomer Rouge the bat, self-proclaimed treasure hunter who was after the Master Emerald until her boss told her to infiltrate Eggman's group and keep tabs on what he's doing, and yet didn't give her explicit orders to
stop him at any point, meaning she actively helps in his plan to take over the world, even at the expense of several members of the militia she's supposedly on the same side as.
Sonic learns of Eggman's trickery and tries to stop him from getting all the emeralds, but being cooped up in a prison means Eggman already has six by the time he's broken out, a fact that Eggman flaunts as he blows up half the moon (in an event that later entries mistakenly ignore by depicting a fully-intact moon) and threatens to do the same to any country on Earth that doesn't submit to him within 24 hours, without any regards to the size of the country and collateral, meaning that while a large country like China could be wiped out without too much issue, if a country like Israel started to act indignant and rattle sabers with Eggman much like they rattle sabers with Iran in real life then Eggman would probably wipe out Jordan, Syria, Egypt and Saudi Arabia at the same time.
Now the stage is set for an action-packed adventure where you can either save the Earth as Sonic, Tails and Knuckles (who is mostly after shards of the Master Emerald after he deliberately broke it to prevent it from falling into the hands of Rouge and Eggman, the latter trying to steal it without thinking about how the laser cannon in the ARK only has slots for the seven Chaos Emeralds and not a giant honking one for the Master Emerald), or destroy the Earth as Shadow, Eggman and Rouge across three different gameplay types - Speed (basically Sonic's story from the first
Adventure, but arguably better), Shooting (basically Gamma's story from the first game, but with a health bar and without the countdown timer that's extended by shooting combos) and Hunting (basically Knuckles's story from the first game, only much worse since you have to go for the emeralds in one very specific order and can only stumble upon later pieces by sheer luck), only you can't choose which order you do the gameplay styles in unlike last game, as you're forced to play as a given character at a specific point in the plot whether you like it or not, with the only choice being whether you see the plot from the heroes' side or the villains' side.
There, five sentences. Now, about those Chao...