I don’t blame SEGA if they are trying to act like the game didn’t exist.
If they're doing that, then they don't seem to have any problems with referencing it. They remixed the main options menu theme and Westopolis for Sonic Forces and there was a theme for the 3DS that had Shadow The Hedgehog vibes to it. It had a burning city and the folders had the Black Arms/Shadow insignia on them. Heck, the original options theme was even used as the music for the theme, which I personally have no problem with that.
As you have all stated, SEGA is distancing themselves from that game, though it has also been thirteen years since they released that game. They had a good concept going with Shadow joining G.U.N. after that game, which is set before the essentially non-canon Sonic 06. Technically he is still a member of G.U.N., as in-game dialogue in Sonic 06 suggests that he had joined years prior to the events of the game; yet with the recent characterization for Shadow in recent years, I somewhat doubt this is still true today. With SEGA wanting to make Shadow into a mean character, Shadow's qualities as a hero are all but gone.
It's a shame, seeing as they could have made another game for Shadow with his characterization from Sonic 06 and earlier (except from ShTH), fighting as an agent of G.U.N. and potentially having newer enemies to fight (Yellow Shadow Android and Infinite come to mind). They could have also resolved the plot-hole of why Shadow was actually created; remember that he was created to be a cure for Maria's disease. They could have shown how Shadow was adjusting to working toward helping humanity, or even give G.U.N. a larger role as support for Shadow or something, or even expand Shadow's relationships with Rouge and Omega as friends and partners.
Sometimes I wish that SEGA didn't start using only Sonic for their games.