Nintendo

There was a span between Ocarina of Time and Twilight Princess where each game treated previous ones as established history. The handheld games have always done whatever; Link's Awakening is a direct sequel to Link to the Past which is all a dream, it's directly in the text of that game. The Oracle games take place outside Hyrule, Minish Cap takes place in Hyrule but the distant past, so we can largely ignore them as side stories.

Ocarina of Time, especially given how tremendously popular it was, became an anchor point for the series. Majora's Mask is a direct 20 minutes later sequel which is almost like Link's Awakening. I subscribe to the fan theory that it's Link's dying fever nightmare. Wind Waker and Twilight Princess both treated Ocarina of Time as historical events that literally happened, even if they mutually ignored each other. I think that's why they did the multiple timelines thing, just to reconcile WW and TP.

You can just feel them wanting to shrug off the timelines thing from there; Phantom Hourglass and Spirit Tracks are direct sequels to Wind Waker, Link Between Worlds is a direct sequel to Link to the Past of all games, Skyward Sword is a far past prequel, and then Breath of the Wild and Tears of the Kingdom are a reboot of the series.

But from about '98 to '05 or so, it felt like a series and not a franchise.

Wanna hear my juiciest Zelda conspiracy theory? There are several pages of lore at the beginning of the manual for A Link to the Past, I have the North American version of this, and I don't know how much of it was written by Nintendo themselves and translated or how much of it was written by Nintendo of America (I know Ganon's last name "Dragmire" was made up by NoA) but the whole thing retroactively reads like a design document for the rest of the series. Seriously go read it and try not to think "Holy shit this was written in 1990."