Sick crossover time: Mechina's "As Embers Turn to Dust" storyline is the bad end of Sora. This wall of text that nobody but me will understand was brought to you by: autism.
In the storyline of both, a global war wreaks havoc on the Earth, threatening to render it inhospitable to life, fought between dogmatic factions that have been fighting for ages. Mechina focuses on the factions, which are essentially just Crusade memers fighting against Super ISIS. Sora doesn't really focus on the warring factions and instead focuses on one of the super-soldiers, so it doesn't necessarily contradict the two's compatibility. However, in the deployment of the super-weapon is when the timelines diverge. In Sora, she manages to stand up to Star Breaker's assault and is frozen in ice after defeating her (or something like that). However, if Sora didn't stop Star Breaker, then she would have most definitely destroyed most if not all of life on earth.
Fast forward to Interrugnum. This song is someone returning to the ruined planet Earth and declaring he will be the new ruler. This is clearly Shifu, returning with his ship. If Sora succeeded, then he would have encounter the Brand New Earth and Suguri, but in this timeline, the world was rendered barren. Despite that he decides to plant the flag of conquest, trying to create a new Earth on the ashes of the old one. In this case, Shifu is the true name of the Soldier of Earth whose memories are used to repair Amyntas later on in the storyline.
With Conqueror and Empyrean being flashbacks leading to Sentient 2145 realizing he is in fact Amyntas, the story shifts focus away from Earth and towards the Titanborn - Which were humans that "died" during space travel but were merged with the ship AI that carried them. This explains what exactly Hime was as well, since she was the core of Shifu's ship and Sealed Guardian or something was just another name for Titanborn. Of course as we all know Amyntas (or Half-Shifu) then goes on to regain his true memories and go back to the inter-colony war and we all know how that turns out.