STH3&K's Canon Ending And Hyper Sonic Is Canon
So in one of the cutscenes for Sonic The Hedgehog 3 & Knuckles we get to see that the canon ending to this game, is the one where you collect of the Super Emeralds and become Hyper Sonic and fight Eggman in Doomsday Zone.
Also, Sonic Channel's Super Sonic info says the following about STH3&K.
"By collecting all the emeralds in the main game, you can transform into Hyper Sonic, which is even more powerful than Super Sonic."
So yeah Hyper Sonic is canon, however it doesn't show up anymore to avoid DBZ comparisons from what has been stated.
An in-universe explanation could be that the Chaos Emeralds must be charged up into the Super Emeralds by the Master Emerald, and Knuckles doesn't let Sonic do this as he himself won't use the Master Emerald for himself.
Extra note, while it was claimed that the Hyper Forms aren't canon this wasn't ever actually said.
The claim originates from GeneHF on Sonic Retro's discussion boards, the one titled Sonic Runners announced (Sonic Team/Mobile) which was started Dec 28, 2014. Credit to definitivedubs post on Sonic Retro under the title "Only male hedgehogs can turn Super" made Feb 21, 2023. As they are one was able to find where this claim originated. So GeneHF claims that "The Super Emeralds and the Hyper forms are non-canon. They may never be referenced again." They also claim that this is from the Sonic Bible and that Iizuka said this stuff publicly, but provide no source. Note, I'm not addressing the Sonic Stadium stuff because that literally leads nowhere.
Written by Eris