>The shows couldn't be further apart in style and tone.
Very true, but luckily they don't have enough continuity to really make it impossible. Sonic & Tails deal with Robotnik's more minor schemes, with bumbling henchmen like Scratch and Grounder, Monday through Friday, but Robotnik saves his really big plans for the weekend, and that's when Sonic & Tails need to go find their friends The Freedom Fighters and work with them to stop Robotnik's more serious schemes.
>You can't make Sonic Fighters and SatAM/Archie and Adventures and all the games canon with each other because it's never going to work.
Of course not. SatAM/Adventures is its own continuity. Archie is its own continuity which is heavily based on SatAM/Adventures but not actually the same thing. The games are and always have been their own thing, with only Spinball and Mean Bean Machine ever even referencing any other continuity. Except for Amy and Charmy being in the games despite originally being from a manga. But they're heavily altered from their manga incarnations, so as to make them fit in the games' world.
>This worked for the Star Wars community for a long time. You pick which novels work best and ditch the shitty comics that conflict and get bogged-down with dumb ideas that go nowhere.
No, Star Wars had canon-tiers, where what was canon depended on what medium it was. Movies were top canon, followed by novels, followed by games and stuff. Then Clone Wars came out and was above the novels. I forget where shows like Ewoks and Droids went. I mean really they should be above the novels with Clone Wars, but since they're less serious, I bet they weren't. Anyway, things of lower tiers could be said to count, unless they contradicted things of higher tiers, then those details didn't count. When making higher tiers, creators, especially Lucas making the movies, didn't give a fuck about lower tiers.
Sonic could be said to be similar, in that the people making the games obviously don't give a flying fuck about any adaptations, except for the ones mentioned above, and even then, it's not like they just treated those things as canon.
But no, seriously, Sonic games have a very tight continuity, except Spinball and Mean Bean Machine. Fighters is honestly the biggest problem, because of the 8 emeralds. But again, that's really not the biggest deal, and it's easy to say one is the Master Emerald. Aside from that, the biggest problems are things like map screens showing recurring locations as being in different places, which still most people wouldn't notice, except for maybe the most egregious example of Forces showing Green Hill as being on the mainland instead of South Island. But even then, only big nerds who actually know Sonic lore would know what South Island is, since it's never talked about outside the manuals for Sonic 1 and a few Game Gear games, and isn't even important to the lore compared to Westside Island and Angel Island. And Westside Island never has its name spoken outside the manual for Sonic 2 anyway.
Of course, the games starting with Unleashed, and especially Colors, go out of their way to not have very complex stories. But they do still make references to past entries, and since they don't have very complex stories, it's not like they really contradict earlier ones. And obviously, having minimal story does not mean that it's a new continuity.