That's the thing, you don't qualify for being a "Star of the City" as in the title, Hana Association designates you as one.
Valecina was never designated, so you can't use Rien being designated as one to say all Nursefathers are. She has her own feats of being in that general power range, but not the actual title.
Their first encounter was Valecina using Charon as a meatshield to stop Vergilius from killing her and it ended with her being exhausted and Vergilius completely fine. She is not on his level. In fact Valecina was rather explicit about needing Charon to avoid dying.
No, she has
Precognition (via the Eye of Odin's calculations). The Eye of Odin doesn't do anything other than that (and blinding + hurting her in one eye if it overheats).
She downscales enough that she can put up a fight, but that's about it.