Here's the long, messy truth: canon can mean a lot of different things depending on who you're talking to, and that makes 'Re-Awakened: I Ascend as an SSS-Ranked Dragon Summoner' a tricky case to pin down.
From my corner of the fandom, I treat canon as whatever the original creator explicitly confirms or whatever the original serialized work includes. With that in mind, the safest framing is that the core web novel (the original serialized chapters) is the definitive timeline. The upsides of adaptations—manga, manhwa, official spin-offs—are that they bring polish, art, and new scenes, but they often rearrange events for pacing or audience appeal. For 'Re-Awakened: I Ascend as an SSS-Ranked Dragon Summoner' specifically, the adaptation is officially published and carries the author's blessing for many of its major beats, yet it also introduces side arcs and character interactions that never appeared in the raw web novel. That makes it semi-canonical in my book: the main plot points that the author approved feel canon, while the added scenes and a couple of continuity tweaks read more like authorized embellishments rather than strict, unquestionable history.
So if you want to geek out about worldbuilding and character motivations, you can reasonably include the adaptation as part of your personal canon, but keep a foot in the original text when debating strict lore. Personally, I enjoy the extra flavor the adaptation brings even when it diverges; it feels like getting a director's cut of a favorite movie, and I’m happy to treat it that way.