Soukou no Strain/WMG

The story takes place in the far future of Rozen Maiden
And the Emily dolls were designed from blueprints of the Rozen dolls salvaged by the Union, only with the MIMIC cores installed where the Rosa Mystica would be. One of them did look an awful lot like Suiseiseki.

The Grabera trio are artificial creations of the Emilies.
The last living ones see Sara as their hope, and having gone into Ralph's mind, they knew about her before meeting her. Knowing the trauma that she would go through when Ralph came to save them, but unable to do anything about it, they managed to contact a mechanic while imprisoned, who built three friends for her. Considering their similarities to members of the Space Squadron (especially Cedie to Carris, which is pointed out and jars Sara into considering becoming their friend), they might have been created to give Sara a clue of who to turn to in order to break her out of her Heroic Sociopath stage.

The Emilies are descendants of the Frontier fleet.
Ranka and her descendants evolved into a Human/Vajra hybrid race, with telepathic abilities. They lived peacefully until they encountered certain other humans...
 * Where did all the Fold tech go?
 * The Vajra ate all the fold quartz.

The show takes place in the future of Code Geass.
The mecha designs are rather similar; those of STRAIN look rather like what you'd get by taking Knightmare Frames and advancing the technology.

The animators heard about the Hide Your Lesbians trope and took it literally.
Thus why there are so many scenes in the later episodes where Lavinia is absent (or perhaps merely offscreen) for no apparent reason.