1. "Why did she do it? Why did she jump out there alone and try and fight the guy that just flattened the village like a pancake?" I've already discussed this before, but Sakura's expression was not directed at Hinata as a person. It was a realization that other people like Naruto too. It was not resentment or stupid jealousy. It was a thoughtful moment for Sakura and made her reflect on Naruto in general.
Hinata seems to love Naruto as she jumped out there and and risked her life for him, maybe she should do the same? Will others do the same for Naruto too? If Hinata's confession influenced Sakura at all during her confession, all it did was encourage her to go and risk her life to kill Sasuke for Naruto's sake, which is far fetched.
Unless Hinata's personal talk no jutsu was projected for the entire world to hear -or I'm missing something- no one heard the actual confession save Pein and Naruto. Others might be a bit confused why she randomly jumped out there, but Sakura ties 2 and 2 together.
Of course, she wouldn't know about the confession absolutely, she's probably making an assumption, a big one. Why would she have any reaction towards Hinata if she didn't actually 'witness' the confession in a hearable range. Even if she did hear it, what do you expect Sakura's reaction to be like?
"Oh Hinata, I heard you like Naruto now. Just to let you know, I'm watching you. You better not try anything with him", "I heard you like Naruto too. We're now love rivals"
Hm, what does that sound like to you? Oh I know, the 12 year old Sakura that you admitted she no longer is. What would she ignore Hinata for? Hinata hasn't done anything wrong other than love a boy she's hardly talked to.
Sakura isn't going to have any reaction towards Hinata that is dramatic and I think you're putting way too much thought into moments that aren't important.
4. She hasn't fangirled Sasuke since part 1. Just making that clear. She still might love him yes, but fangirl Sakura is gone. She's blended in with her inner self, no longer hiding behind a fangirl personality. Again, she's not 12 anymore.
So you expect Sakura's reaction to be "OMG, You're the Yondaime's son?! We should totally get together now Naruto! Because you're so cool and famous and the son of a hero even though you're already a hero yourself! Sorry for slapping you when you needed it! How silly of me! *giggle*" -the above example is exactly why I avoid some NS fanfiction. They have this type of horrible unrealistic OOC reaction from Sakura-
The only effect it could have is Naruto telling her for the sake of telling her more about himself. Just having "Minato is my father" on his resume is not going to boost Sakura's romantic interest in him. Neither will it be a negative one.
The only reaction I can see is maybe a bit of sadness, realizing it was his own father that sealed the Kyuubi in him. No fangirling, no checking off a resume list, no disgust for Naruto all the sudden, nothing as dramatic as you see to want it to be. It would probably be a serious or serene moment between the two, maybe others.
If she cared about hitting the relatives of Hokage's, then she wouldn't have hit Konohamaru in the past and definitely wouldn't have hit him for his yuri no jutsu. No one cares that much about being the relative of a Hokage. They aren't gods, she's not suddenly going to worship the ground that Naruto walks on. And she's not going to be sorry about knocking some sense into his head NOW AND THEN. -seriously she doesn't hit him that much and it's all comedy relief

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