Sonic '06 actually has some of the best story in the series. Shadow is at his peak, and Silver's story is good too. It's just Sonic's story (especially with Elise) and the gameplay that ruins it. Mostly the gameplay. But even with the gameplay problems, the level design is pretty good, as you can see if you play the Project '06 fan remake.
Sonic Colors DS (not playable, but story relevant)
These are the only games where Shadow is actually important to the story in anyway.
Not the ones where he's playable but the ones where is playable AND story relevant
(In Sonic Boom he is a cameo at best... but before Sega took over what Big Red Button was cooking it's implied he may have been leading a faction of the Black Arms)
And here I am only with SA2 and Heroes experience. I'm thinking to do the runs soon since retroachevements started supporting GameCube, and I found a Shadow the Hedgehog: Reloaded mod that's highly praised and supported.
It's like they were prepared to make Shadow 2 but Shadow 1 didn't realize that didn't do so well so they pretended Sonic had anything to do with the story.
Yeah but Sonic barely has any interaction with Silver outside of one fight and the latter going "Oh wait you're a red herring and Memphis Tenessee is a dickpenis."
Blaze doesn't even go "Oh hey Sonic. Remember Sonic Rush? Me neither."
They fight in the city, yes. Then they almost fight at Radical Train, but Shadow gets in the way. Then they meet up and go through Kingdom Valley together, then when the Egg Carrier crashes, the two of them go back in time together so Sonic can stop it. That's more interaction that Silver and Shadow have I think.