It's questionable that it's not literally just a fan theory. For years fans were trying to put the Zelda games on a single timeline, and Nintendo just didn't care. The split timeline was one of the top theories of how everything can be put together, based off of a single developer comment that implied a 2 way split instead of a 3 way split: https://zelda-archive.fandom.com/wiki/Split_Timeline

Then Hyrule Hostoria came out as a collectable. I would put good money on a conversation during its writing that went like this "What else can we put in here?" "Maybe a timeline of the games?" "Yeah, sure. What's the official one?" "There isn't one. The fans have a fun split timeline one." "Oh neat. Yeah work out the details. Now has anyone found that Wind Waker concept art yet?"

A common flaw I see in media literacy is operating like the author has pulled a completely coherent story from a different universe and simply written it down, as opposed to a creative process. Nintendo has never cared about the timeline, nor developing a single coherent story across all of the Zelda games. Some games are sequals, prequels, or have direct references. The timeline itself is purely from non-game sources, and is obviously not a factor when they design a new game.

Yes, but published very much due to fan pressure, and clearly figured out to match the games rather than being designed up front. Nintendo perhaps more than other Japanese companies intentionally avoids letting existing lore constrain their creativity on new games. That apparently is changing however, as now that Nintendo has successfully launched a cinematic arm they have said they want the movies to be a source of canon that the games will reinforce, a markedly different strategy than they've used previously.