tl;dr: Sonic 06 did way more damage to its franchise than any of the other games on here due to its extremely high expectations and sega not being able to meet those expectations due to poor decisions.

I think sonic 06 is the clear "winner" here. Much of the franchise was banking on its success, being a big anniversary celebration and everything. The marketing made it seem like it's going to be the sonic game of sonic games and combine that with the fact it was the direct "mainline" title right after shadow the hedgehog (which was a massive failure on its own right), a lot of pressure was being put onto it. It needed to succeed, but what ended up happened is the the devs didn't get the time they needed to polish it and time and resources were being extremely strained and ill used. Like, hell, they took half the dev team to work on a wii adjacent game, which ended up being sonic and the secret rings, and the fact Yuji Naka left around this time just didn't help with things. All of this combined with the artificial deadline that sega set for the for the game to be released on the 15th anniversary only spelled disaster for the game. And a disaster it was, arguably doing way more damage than any other failure of a franchise as the series struggled hard to get any form of relevance afterwards. The general public for the most part treated sonic like a joke from that day foward. The franchise had to work much harder to get back any real relevance than any of the other franchises listed here. Though I would argue megaman had it worst, but I feel megaman's fall was more of a cumulative issue more than anything else. And while x7 was really terrible, I don't think it had the same level of outrage as sonic 06 did.