The connection between Mitsurugi Meiya and Tsukuyomi Mana is arguably one of the most delicate things in Muv-Luv. While on paper, it is your typical master-servant trope, but as the story progresses, there is more to this than meets the eye. I’d say their relationship is something that falls between the line of sisters and mother-daughter. Neither of them chose this path, yet they continue to strive in life.
One learned to attain something, the other, let go.
Mana poured all her heart and soul into guiding Meiya down the path of light, which ironically is part of the procedure to create a perfect body double, aka shadow, for Yuuhi, whose role is to "illuminate" all of Japan as her name suggests. Though both of them were fully aware of the grim future lying ahead, they pressed on.
Never displayed grief and the likes on the surface, Mana is a legit hardened soldier in every way. Nonetheless, deep inside, she's always in a great conflict with herself. This endeavor might be part of her duty as a member of the Shogunate, but the feeling and emotion that she put into are real, just for Meiya, and Meiya alone.
However, nothing lasts forever. A bird kept in a cage is no bird. It was Meiya’s destiny to go out there and find herself. Half of her life was indeed nothing more than living as a political hostage. Nonetheless, Meiya always held her head high and spared no effort in seeking out a meaning for her life.
Therefore it was incredibly cathartic to see Mana sending Meiya off to the path of her own. The atmosphere was so majestic, heroic, and tragic at the same time. Having one last warming conversation was too much of a luxury for these women of war. The two of them had spent far too much time together to get sentimental in such a dire time. Hence, having known full well of that fact, a single nod was all it took for them to bid each other farewell.
Such is the world of Muv-Luv Alternative. Such is the world where people take drastic action instead of making fancy speeches. That said, while they might have appeared to accept this outcome, let's all be honest here, none of them deserve any of that harsh reality.
Yep, this is cliche. The same kind of story that had been told over and over again, heroes going to war and die fighting for their loved ones, nothing new, nothing special. Nonetheless, under the setting of this universe, especially with how these two amazing women had been portrayed and foreshadowed in Extra, the painting depicting them in Alternative is just that spectacular.
IMO this is also one of the "true love" that Kouki was trying to convey to readers throughout the story. There are certainly more coherent ways to define that term. However, the bond between Mana and Meiya just resonates with me the most, thanks to the subtle build-up and conclusion.