When you refer to Dark Shadow, you talking about when he's Glowing Red and Such. I think that's something that now happens when he just takes off his Inhibitor Rings, as Seen in Sonic 06 and Sonic Boom
In any case, I do imagine it would be apart of Shadow's Moveset, but not as his Final Smash. I actually imagine it to be apart of his Main Moveset as a Transformation of sorts. Since Shadow can technically release the Rings at anytime, and to make this transformation more unique from the rest, I Imagine it to be a Transformation you can activate at anytime, Which buffs Shadow stats, gives him better variations of certain Chaos related moves, and access to Chaos Blast
The downside is that Shadow takes more Damage and Knockback in this mode, He takes damage overtime after certain amount of time, and Chaos Blast is the only way to exit the move, which has alot of Endlag
Dark Shadow is specifically from his own game. It's part of the alignment meter. It leads to Chaos Blast if you're at full darkness. Hero leads to the best Chaos Control move in the game.
And yeah, his "unleash his full power" is interesting. That could also be a neat Final Smash. That's not too unlike the concept with Hero and Dark mode, but a different power source. His Chaos Energy thingy in 06 is pretty much a weak version of removing his rings. I forget if it was called Chaos Mode or something else. The inhibitor rings have come off in Adventure 2 and Sonic X as well. He also can use his chaos powers in Battle even when he doesn't have a Chaos Emerald(in the story, he gives the last one, his own, to Emerl, saying Maria in his heart is where he gets his powers). It's still a clear case of Gameplay and Story Segregation. He has an Emerald throughout the rest of the story.
Yeah, Shadow the Hedgehog's Chaos Control, you basically cannot complete The Last Way without that move so you have to get used to it.
But Sonic Battle, I love the Special move he does where he disappears for a second then comes back and goes "RNNNNN" and fires off that huge Chaos bubble wave that sends people flying.
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"Didn't even break a sweat!"
Then Eggman shows up in story mode and literally goes "Prepare to die!"
Actually, in the Japanese version, ROUGE is the one with the foulmouth when addressing Eggman.
Sonic Battle is actually in my top 5 Sonic games, I love it! I actually believe it got more play time in my GBA than Pokemon Sapphire did. I played that thing CONSTANTLY!
I won't lie, the last story was a bit tougher. I only had issues with finding some keys, certain missions, or not running out of rings in the final battle itself.
I love the game, though. It's a fun cheesy one.
Chaos Burst is an amazing move, and it's pretty much a weaker version of Chaos Blast. Shadow's game does lead into Sonic Battle story-wise, so it makes sense why he can do that. That said, Chaos Burst obviously inspired Chaos Blast in terms of development(Heroes and Battle were closer to the same development time instead. This is why Rouge notes that Chaos Gamma has Gamma and Omega's parts).
Rouge is the most mature age-wise of the normal Sonic cast that isn't human. It's not too surprising she's a bit more foul-mouthed. She literally added fanservice to the game, and is basically a dominatrix personality. Of course, ignoring everybody swearing in Shadow(I can believe that from some. Shadow, easily. Espio is a ninja, and I can slightly believe it since they're battle-hardened and not necessarily supposed to be "nice". Eggman, to some degree, but that's cause he has multiple interpretations. Rouge a bit. Sonic no, but oddly he does say the swear version of crap in the Japanese Sonic X, but that's not the normal games. Some just were awkward where they sweared, since it doesn't fit their personalities well.
Eggman actually isn't too odd saying "prepare to die". But that's due to the various cartoons, two of which make him very vicious(SATAM and Underground), to the point he's well beyond the general games. Like, Sonic 2 has a pretty dark-looking Robotnik image, but he's still pretty cartoony within the game. Now apply that as his personality style, and he's legitimately scary. Even when he's partially a butt monkey(Underground), he's very easy to take seriously. He's more comedic in most adaptions otherwise(X and Boom), while still being serious when he wants to be. The only one he's pretty much a goofster is Adventures of Sonic the Hedgehog. Well, he's deadly serious in the Sonic Movie too, and the OVA has him pretty much like Sonic X, a good mix of both. But it's the only other animation adaption based much more directly on the regular games, so that's not that surprising.