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Is Suisei potentially just way more embarrassed about being seen as being in a steady relationship, whether it's real or not, than Miko?
The animal icon incident and how she tried to worm herself out of it during the trial, saying people will start saying they're gachi, makes me think that way. She also likes less Micomet art than Miko in general and basically goes an embarrassed "N-no" when put on the spot by Flare and the rest of Shiraken.
We know that she is not at all an alpha stacy who is unfazed by others but instead is just as much of a sweet little baby who wears her emotions on her sleeves. And if we believe that she has never been in a relationship before, then it makes a lot of sense that she just doesn't know how to handle it and business is her self defense mechanism to avoid being put on the spot.
It definitely seems to me like Miko is much more comfortable with the idea of teetee.