Charitably, one could say she’s trying to form a connection with you using any topic to hand. However, the fact that she can’t assimilate your schedule is a barrier.
Some people, no matter how plainly you tell them things, they don’t think you really mean it.
And good morning.
I recognize the attempt at the connection, but the lack of ability to accept someone’s boundaries (in this case, schedule [British pronunciation]) reeks of narcissism. Abusers have no concept of boundaries.
Probably the best way to get her to internalize your schedule would be to text her a cheery “Good morning!” when you wake up.
First thing.
In the middle of her night.