Distant Future (BOTW / TOTK)
Ten thousand-ish years past every branch's end — and Nintendo deliberately won't say which branch leads here.
Fork point: Officially unspecified — Nintendo has never confirmed which branch it descends from
The Story Arc
Breath of the Wild and Tears of the Kingdom sit at a distant-future point after all three branches — and that's all Nintendo will commit to. Asked directly which timeline they descend from, producer Eiji Aonuma answered: 'That's… up to the player's imagination, isn't it?' The stance was extended, on record, to Tears of the Kingdom — 'a puzzle the users will have to see if they can solve.'
In-fiction, this era is defined by cataclysm and memory: the Great Calamity that broke Hyrule a century before BOTW, and the far older Imprisoning War against Ganondorf that TOTK unearths along with the Zonai. The deliberate ambiguity isn't an oversight. Nintendo drew a chart for the first eighteen games — and then chose to stop drawing.
Games, in chronological order

Breath of the Wild
A century after Calamity Ganon devastated Hyrule and felled its Champions, an amnesiac Link wakes to reclaim his memories and free Princess Zelda, who has held the Calamity at bay alone the entire time. Nintendo places it at the distant-future point after all three post-Ocarina-of-Time branches — but has never said which one it descends from.

Tears of the Kingdom
Direct sequel to Breath of the Wild: Link and Zelda uncover the ancient Zonai civilization and the truth behind Ganondorf's imprisonment, as sky islands and a vast underground 'Depths' expand Hyrule vertically in both directions.