I think it's set in the Child Timeline after Twilight Princess. Not only we can clearly see some parts of the world that strongly resemble that game but also the game is set on a world in ruins and in a state of decay (confirmed).
Not to mention the use of technology as opposed to magic. That's one of the focus of the game, implying it's set in the future. I know Skyward also had technology, but it was a very different one... this is related to Sheikahs advanced gadgets/tech. The ancient tech of Skyward is also kind of lost in the next games of its timeline and there are many reasons for that.
Plus, there were statues activated by some sort of magic/tech in Twilight that remind me of Breath of the Wild a bit:
Spoiler:
On a site note, there are some evidence/possibility that we might travel back to the past in this game.
Bet with Teeqoz for 2 weeks of avatar and sig control that Super Mario Odyssey would ship more than 7m on its first 2 months. The game shipped 9.07m, so I won
