Memes aside this is actually really baller. You've managed to make him feel distinct from Sonic while also feeling like a classic style character.
While not a criticism (believe me, there's absolutely nothing to criticize here, this is a phenomenal effort), Shadow not having Lightspeed Dash feels a little unusual to me, since I've always associated that ability with him more than I do with Sonic. That said, there's not really as much of a place for it in SRB2 with the way the vanilla levels are designed, and while other released characters have it, it tends to be just another thing they can do. Or in the case of Modern Sonic, part of trying to give Modern Sonic everything that Sonic has ever been able to do in a 3D game.
It took me a minute to wrap my head around Snap, but once I did it was glorious. For anybody who understands the comparison, Snap makes Shadow feel like Vergil from the Devil May Cry series. Said character is the only one in the series to not have a double jump, but is able to do like Shadow does in this mod and teleport up or down or to the side at a whim, or to a nearby enemy, granting him hilarious combat mobility once mastered.
While not particularly relevant, I thought it was a fun coincidence to see two edgelord rival characters share such a similar ability. Once I understood just how mobile Snap makes Shadow, I actually felt a little overwhelmed by the power given to me, not to be too overdramatic.
The trick animations also got a genuine chuckle and smile out of me when I was in a pretty sour mood while briefly checking this out.
10/10, he feels like he could be an official part of the game, from the sprite work to the mechanics. If I didn't know any better, I'd think he actually was.