Like as of the latest book to be translated to english Akari and Menou's relationship has basically been (spoilers)
Akari: *actively declares undying love and attraction towards Menou, constantly*
Menou: 
Akari: *actively conspires to die in the hopes of saving Menou's life, while burning her literal soul as fuel to keep a three month timeloop going for an unknown number of years in the hopes of finding an iteration where Menou lives* (corny as that sounds, the gradual reveal that that's what was happening was great)
Menou:
Akari and Menou: *merge their literal souls together, becoming one singular being split between two bodies, in language that's explicitly romantic and euphemistic*
Menou: "I made a friend."
Akari: *gets mind-wiped by the original Menou, Hakua, who is both the literal god of the world's main religion and so madly infatuated with Akari that she betrayed and murdered every other friend she ever had, waited a thousand years, and plotted to kill an entire world just in the hopes of being reunited with Akari*
Menou: "I must kill god, alter the basic mechanical rules of this world, and save my friend. Then I will spend my life with her and hold her hand, as is normal for friends."
I want to scream. 
Still a shame the anime never got picked up for another season.
New headcanon: Menou is ace and also got no sort of sex ed whatsoever and so literally thinks holding hands is as intimate as it gets, a misunderstanding further compounded by her soul merge thing literally involving holding hands.