The Homing Attack origins from Sonic 3D Blast, NOT Sonic Adventure 1.
The Fire Somersault is no difference from having the Fire Shield on and just doing a small Spindash.
Flying Kick really isn't anything different from Aerial kicks in multiple other games, it just means he could Kick.
You forgot Ancient Light, which is a remake of Light Speed Attack, but only works on enemies. Light Speed attack is used to do the original Light Dash, as Adventure 2 added Shoes that gave him the instant ability.
Bounce Attack is the same thing as using the Water Shield in Sonic 3 to Bounce. It did not origin from Sonic Adventure 2.
Sonic can barely use Chaos Control, so we don't consider him a full user of it. It's Shadow's move, end of story.
Spin Attack is the original Spindash, just in 3-D. That originated in Sonic The Hedgehog 2(Genesis/Megadrive)
Time Stop is not Canon and doesn't count.
Mystic Melody really doesn't fit into Smash, but it did originate from Sonic Adventure 2(to my knowledge)
Super Boost/Rush is pretty much the same as Rocket Accel.
Sonic Wind is homing and it is possible it was reused for both Shot Attacks in Sonic Battle.
Triangle Jump is new but useless in Smash.
Blue Tornado is actually useable as a decent Up B, but not all prefer it.
Sonic Rush's two Tricks really only give him a second jump for Smash.
In other words, the only new abilities are Rocket Accel, Triangle Jump(useless), Hop Jump Trick, Humming Top Trick, Magic Hand, Chaos Control(useless), Time Stop(useless), Sonic Wind, and Light Speed Attack.
Thus, not much is useful other than the already done movelists. Maybe a list of ALL his abilities thoughout ALL of the games would be useful.