My read of this is that Miki's boyfriend breaking up with her for being too clingy created a fear of abandonment. She clung to Aki in the belief that sisters will always be closer to one another than anyone else, but now that Aki is dating Shiho she's realizing that won't always be the case. I think the grief she's feeling is a reflection of that feeling of abandonment.
I'm not really sure Miki's feelings for Aki are entirely romantic, but it's easy for her to jump to that connection because the specifics of what she wants from Aki - a desire for exclusivity and deep emotional intimacy - overlap a lot with romantic relationships. I have a feeling this arc is mostly going to revolve around exploring that difference.
I agree with you!! As someone who has a fear of abandonment, I recognised the reaction she had when Aya told Miki that she was dating someone. If the person I am closest with (sibling or a friend) would tell me that they had found a partner, I would absolutely feel mixed about it. Ofcourse I am happy for them! But I am also scared I might be seeing that person less. Things will change, it will not be how it used to be. And that on it's own is immensely scary. Scared that I might drift apart from them. And scared I might be seen as lesser than her partner.
People jump the gun to incest too quickly since Miki is not disclosing her feelings for her sister to be romantic. But do mind people, she is a teenager still. They all are and from what I gathered, they all had to figure out what their version of love is. Like with Himari at the very beginning, she loved Yori's singing, she loved her but- not romantically. And that took her a while to figure out that there are different types of "love".
I think that the author will be using and applying this mindset to set up the situation. Because we all have been noticing the adoration Miki has for her big sis. She's someone that she looks up to and treasures dearly because she was there when she was at one of her most vulnerable moments.
Not every type of love has to be romantic and I think that's what the author is going to teach us. That love can also be non-romantic.
And if I am wrong? Well that would suck wouldn't it?