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.
This ^^^
(Also thanks for the chapter!!! Putting this up here so it doesn't get buried underneath my Long Ass Comment)
The complexities about human emotions cannot be so easily fit into one box. Obviously not all people's experiences are the same, but I've had times when peoples I've gotten close with have gotten partners themselves and I'd feel an intense jealousy over it, even wondering if it was due to underlying romantic feelings I wasn't aware about. In hindsight, it wasn't, but that's the thing. In hindsight.
It has something to due with feelings of exclusivity, that
you're their closest confidant and alil that. It's the same vise versa; they're your closest confidant so you expect them to always be by your side first and all that. Not being able to monopolize their time for your vulnerability causes a lot of intense, unpleasant emotions to arise.
Like. Due to the dynamics in my family and all that, my brother was the only one who I felt I could rely on and be vulnerable with. When he got a girlfriend, it was weird (understatement) to me that I no longer could reach out to him in the same way because some of his time was focused on another person. I didn't think it was due to any underlying romantic feelings since he's my brother, but the point still stands that this person who I felt comfortable with enough to allow myself to be vulnerable with was suddenly not always going to be there for me in the same way.
Obviously it's ultimately up to the reader's interpretation for how they see this scene, and maybe the extent to which I'm reading between the lines has snowballed into not having connected any dots at all, but that's the beauty of consuming art.