Short answer: No. Long answer: Below the cut.
Let us attempt to derive a definition from use.
My Hero Academia is widely recognized as a superhero manga/anime. But similar series like Jujutsu Kaisen, A Certain Magical Index, and Naruto are not. All of these series (especially JJK) have more in common with MHA than any of them do with, say, One Punch Man, but most people would recognize OPM and MHA as the two superhero series.
And neither of them have any superhero pedigree to speak of, the way Marvel/DC spinoffs and pastiches do; they are superhero series based solely on their own merits. Their genre substance is clearly shonen battle manga rather than American superhero comics, yet they're universally recognized as superhero-genre shonen manga, the way Fullmetal Alchemist is fantasy-genre shonen and Megalo Box is sci-fi shonen.
Very little about the worldbuilding of MHA or OPM maps onto the classic "Big Two" settings. I could go through the details, but I think the differences are obvious; power origins, disorganized hero communities versus formal hero corporations, the place of metahumans in society, etc. But what do MHA, OPM, and the Big Two have in common that other comics don't?
Aesthetics is obvious. If you dress someone up in full-body tights and a cape, they will be recognized as A Superhero, even if they are just a paper-thin context-free character design. Saitama wears a superhero costume, so he's a superhero. Deku arguably doesn't, but other people in his world definitely do.
Context is a bit fiddlier. To paraphrase @artbyblastweave, many superheroes are superheroes purely because they exist in the context of a superhero universe; they stop being superheroes if put somewhere else. Doctor Strange stops being a superhero if you put him next to Yuji Itadori or Artemis Fowl instead of Iron Man and Captain America. Genos would fit into a cyberpunk setting as comfortably as hackers or retrofuturistic computer terminals. Many of MHA's animal-people would work perfectly fine as fantasy characters, even the ones who didn't make it into that fantasy AU ending sequence.
But put a sorcerer and a cyborg and a frog-girl in the same world, ideally with a Superman analogue in the background, and they all become superheroes.
Does Sonic the Hedgehog have superhero aesthetics or context? No.
Sonic would not be out of place if dropped into a mainstream superhero universe. But the same is true of Buffy Summers, or Darth Vader, or Archie Andrews. (I am 90% certain all three of them have appeared in Big Two comics at least once.)
I can't imagine anyone arguing that the Sonic (the character or the series) has aesthetics more similar to Marvel than Mickey Mouse. Howard the Duck isn't a superhero because funny animals are aesthetically superhero-ish; he's a superhero because he mostly exists in crossovers with Marvel characters.
Is the Sonic universe a superhero universe? I'm more open to disagreement here, but I think the answer is no.
Sure, it has a lot of trappings common to superhero universes. Mad scientists and lost civilizations and battles for the fate of the world.
But Eggman Robotnik has at least as much in common with Dr. No or Dr. Doofenshmirtz as Dr. Doom. Lost civilizations are a staple of all pulp-descended genres, and epic battles are common in all sorts of genres.
None of this is distinctively superhero-ish, just compatible with superheroes.
The world of Sonic the Hedgehog, insofar as a franchise with so many authors working without consistent direction can be said to have a world, fits the "pulp sci-fi" mold more easily than the "superhero" mold.