The Japanese Zelda website has seen an update of its official timeline, which now includes Echoes of Wisdom. As a Zelda fan who's into this stuff, it's not all too surprising that they've put it into the Downfall timeline, where you can also find A Link to the Past and A Link Between Worlds. After all, Echoes of Wisdom clearly takes place in the same Hyrule, which has evolved over the ages.
Earlier this month, Eiji Aonuma also talked about how they've avoided the usage of the word "Triforce", in an interview with Famitsu (see NintendoEverything), confirming that the game takes place in an era where the knowledge of the actual Triforce has faded, long after A Link Between Worlds, which is similar to the Hyrule from Breath of the Wild.
However, with all of this in mind, it made sense that they might place this at the end of the Downfall timeline, but that is not the case. It currently follows Tri Force Heroes, which was a direct sequel to A Link Between Worlds (but could theoretically be placed anywhere), but still appears before the NES games.
It's a bit of a contradiction, because this means that the royal family at some point lost the knowledge about the Triforce, but then must have regained it... It's not that this is impossible, it just feels like some unnecessary back and forth. But this placement makes sense for other aspects, where the Hyrule from A Link to the Past is still present in Echoes of Wisdom and later becomes this insignificant piece of wasteland in the NES games. So, for the overall continuity this is probably the best spot, but like with the Oracle games this could change at any point.
It's also nice that it comes after A Link Between Worlds and Tri Force Heroes, because these were the last top-down games and they all share a variety of assets, like certain monster designs. But for the future it would be nice if we were to get a title in one of the other branches, because those have been ignored for over a decade.