In terms of classic sonic, pretty much the only definitive answer to the question would be with Sonic CD's kind of stuff.
However in terms of more modern, post-2000s sonic music I really don't see this thrown around often. When I think of a kind of music style that fits the modern idea of sonic the hedgehog, I usually think of the kind of sample-heavy breakbeat music that naganuma brought to the table in Sonic Rush, which was then essentially revitalized to be more in line with the sonic series by ohtani and nanba in Sonic Rush Adventure. These kinds of tracks really capture the quick, fast-paced action whilst not really 'limiting' itself to a specific set of sounds. What made Rush/Rush Adventure's music so special and so unique was how every sample used was taken from a variety of soundsets, with modern rock guitar samples being overlayed with hip-hop/trance drum beats and even orchestral clips being used once in a while. It really made for a diverse, experimental, but most importantly unique music style that I feel fits modern sonic's character the most. This was even apparent in CD, how it utilized a ton of hip-hop drum breaks and vocal shouts in combination with the old 90s synth patches.
However, I don't think the kind of rock sound that was introduced in Adventure is necessarily unfitting, I just feel that the fact that you can easily classify it as "rock" makes it feel a bit too simplified for sonic the hedgehog. How 06 and a ton of other modern sonic games handled their music is that they simply used kind of 'rock-inspired' guitar licks and riffs with a variety of synths and instruments that aren't usually associated in a rock style.
If I had to pick a second composer that I felt perfectly captured sonic throughout the years, it's Kenichi Tokoi. His work on colours was especially incredible, how he managed to mix up a diverse set of genres for each of the planets. It made a lot of sense that a lot of the songs were drastically different, but they still all had driving beats to give it that quick feel.
Basically, I think the most important thing to keep in mind with sonic music is that:
- It needs to be fast-paced (not necessarily just fast)
- It needs to be diverse
- It needs to fit the aesthetic