I think BotW is of the rumored 4th timeline, one where Adult Link from OoT dies either before he gets to the Ganon fight or by Ganon himself.
The deku tree says that Link has no recollection who he is and he will now tell Link what has happened. (his history as the Hero of Time, his child life among the Kokiri etc)
When Link "killed" he was saved at the brink of death and stored in his slumber by Rauru or any of the other sages.
Ganon who was prevented from gaining the Triforce of Courage as Link never died.
Though Link lives he had lost all his memories.
The Master Sword could be rusty because Ganon had it in his possession for all them years attempting to destroy it before it was stolen and returned to the Sacred Meadow or Kokiri Forest or whatever they call it.
See Hyrule Castle was ruined, it was too in OoT adult timeline. The Kokiri became Koroks to protect themselves. blah de blah
Maybe in an attemp to save Hyrule the sages sealed Ganon in his tower which was built near or on top of Hyrule Castle, his seal lasts until Link awakes.