So ahh, idk if you answer this kind of question, but why did Ryuk go to Earth instead of Sido?
There's a rule that Shinigami can't go to their realm if their DN is on Earth and Ryuk uses this as a reason to stay with Light most of the time, but technically he's not the owner? He's carrying his own DN on his belt. Also, for some reason Light was able to see Ryuk after touching DN and not Sido. I just can't grasp the concept behind this, every shinigami has only one DN attached to them, but if another shinigami takes it it becomes theirs in that moment?
hey, that's a good question and one that's a bit confusing for me to think about as well. I will try to think up a way this makes sense based on the rules we were given, but successor arc canon is extremely fuzzy in my mind at the moment, the eye technicalities and notebook swapping stuff are some of the things that confuse me the most in the story, and I could very well be forgetting some rules or mixing things up. I'm also just getting my list of rules to reference from a Quora answer, since I don't have my manga boxset handy (X). So please keep in mind that I haven't actually gone to dig out my manga to fact check all the rules, and I'm just kinda guessing about this stuff too.
So apparently Ryuk sneakily stole Sidoh's notebook without him noticing and then dropped it to the ground on earth, telling others that it was actually his notebook:
And there's a rule that states any notebook dropped to earth automatically becomes property of the human world now:
So maybe Ryuk stealing Sidoh's notebook and dropping it to earth is like overriding/erasing Sidoh's claim to ownership of the notebook? The human who first uses it once it lands on earth becomes the priority owner of it instead, and then the first shinigami who attaches themselves to that person becomes the notebook's death god. I think Ryuk became that notebook's shinigami since he came down to earth first and touched that notebook and introduced himself to Light.
There's also another rule that seems to indicate that it's possible for a shinigami to claim ownership of another death god's notebook by stealing it or cheating them out of it somehow, so maybe Ryuk owned it already even before Light picked it up:
This particular scenario could be similar to what happens when a shinigami dies while attached to a notebook. If a notebook has no current shinigami owner then apparently the ownership of that notebook is usually transferred to whatever god of death first touches it after that:
So maybe Ryuk stealing Sidoh's notebook and dropping it to earth means that Sidoh now owns zero notebooks, and that Ryuk owns two notebooks... the one he stole from Sidoh, and the one he always has attached to his belt. Once Light gets Rem and Ryuk to swap their notebooks this all gets very confusing to follow for me, and even more so once fake notebooks are also added into the mix. But that's the best guess I can come up with right now lol