Heroes doesn't have much of a story to begin with. He's a good guy, but that doesn't mean he has to be some happy guy like Sonic. Then that game introduces the idea that he might not even be the real Shadow, and the entire point of the next game is exploring that, and giving you choice to control just how edgy he is. So yeah, he can be edgy in that one, but it's up to you. And the canon ending is basically the one where he goes full good anyway. But again, that doesn't mean he has to completely change his personality. In the middle though, I think the story of Shadow the Hedgehog is actually pretty good, with an actual good solution of him deciding that it doesn't matter if he's the "real" one or not, since he is himself and that's what matters. After that he's just in '06, where he's basically just stoic but not very angsty, so much so that the ending of his story is him deciding to fight against Mephiles forever even though he's seen the future and knows that the world turns against him.
Shadow has also been used well in the comics. Not often, but the Shadow Fall arc of Sonic Universe was one of the best arcs Sonic comics have ever had. Having him as a stoic secret agent type works. They could do more of that, and use his less carefree attitude to let him continue to explore the plot more than Sonic would care to, which is precisely what he did in Heroes, Shadow, and '06, but people who never even played '06 say it's bad for the wrong reasons, so now we can't have any of the characters, aestetic, or game play that were in that game. Except the awful Mach Speed sections, which became the only 3D gameplay we'd ever get anymore.