Adventure 1, Adventure 2, Heroes, Shadow, and Sonic 06 are the Dreamcast saga. That's why. They're literally part of the same overall storyline.
Also, same with the Advance Trilogy and Battle. Heroes is a poorly written mess either way. Though I won't deny it massively improved Big the Cat. But they took Amy and slaughtered her characterization to the point of making me gag. Like, really? She was breaking out as a good person who had more than Sonic on her mind. Shadow didn't overdo that, and you can still see her true cheerful and loving self. And 06 continued that, while having her mature enough to not go crazy on Elise due to the plot-relevant kiss earlier. It's an awkward moment, but she truly matured and knew what was more important. Also, the game allows you to choose Elise, meaning they actually wrote her in a mature enough manner so that she could accept Sonic overall wasn't going to be hers. I liked that. The timey-wimey ball, and Elise being kidnapped multiple times was dumb, though. But Silver and Shadow being memetic was nice, and Mephiles is a pretty neat character.
Though you are right, 06 is pretty much Sonic Adventure 3. It does everything the same way, it just lacks a Chao Garden, and clearly needed more time in the oven. I like the game and all, but it obviously has its issues.
Heroes really doesn't resemble the games beyond having the characters and some of the abilities. It's honestly closer to Advance 3 in terms of combo characters. In a twist, Adventure 2 was only going to have 3 characters anyway, so that's kind of a silly coincidence(the 3 character focus per team), though it's still pretty different even then. It was Racing, Treasure Hunting, and Shooting. We lack Shooting, but the Power Characters do resemble Treasure Hunting somewhat. Rouge and Knuckles being different specific roles in Heroes is a funny case, and only Omega does "shooting" as an attack.
Though that's what's interesting on 06. It has Treasure Hunting back, though it doesn't really have Shooting either(Silver might be the closest? Omega definitely is not about Shooting), but certainly keeps the unique roles like Adventure 1 does. Amy finally brings back her magic from the first Sonic CD game. Going invisible was neat, and I honestly liked her gameplay a lot. Shadow felt like a great mix of his old Racing style from Adventure 2, but combined his weapons in Shadow with more polished vehicle gameplay overall. And still had his Chaos powers. Now if only it was more polished(though honestly, the only thing buggy I've found of him is his Homing Attack at best, which can go too fast or too slow, easily losing a life).
I could go on about the bits and pieces, but eh. Few want to talk about the game in any good way, and I get it.