I’m guessing that Suga also has some sort of trauma about birthdays. She’s probably the type to go above and beyond for her GF but it was seen as a nuisance by them. Those bitches don’t know how to appreciate a loving, caring partner.
It’s also worth remembering that she had JUST gotten out of a bad relationship when she moved. Maybe she also likes Miyako but is apprehensive about those feelings. She may feel it’s too soon or that Miyako might see it as a simple rebound.