So, the Movie DLC of Shadow Generations was released. I have not played or watched a gameplay yet, but the plot seems to be exactly what I imagined:
With the DLC installed a giant ring appears in White Space for no aparent reason. Shadow crosses it. Appears in the movie universe probably during the scene in Tokyo. Defeats all the robots that try to kill him and returns home never to mention it again.
So, apparently the writer or someone else has said that it is probably non-canon to either the game or movie universe according to the wiki.
However I always get the impression that when asked, the staff (even if they are writers) of the different movies, comics, games, etc. doesn't have the same definition of canon that we do or at least doesn't understand what it is meant to be.
I am not sure if they just mean that it is non canon because it has no relevance to the plot of SXSG or StH3 and it is never going to come up again. By the looks of it, seems bizarre, but not technically impossible, that Shadow just traveled to the movie universe and came back. Also note that they dropped a teaser of a game called "Sonic Racing: CrossWorlds" were Shadow crosses a giant ring that is a portal, implying that this is how they "cross worlds" so it seems that the multiverse is going to be explored more and giant rings are going to be consistently a form of travel between worlds (Or maybe I am reading too much of a 30 seconds teaser that is probably not even going to be an in-game cutscene).