My issue with Sansa in the show is she thinks she should get all this credit. The problem is she doesn't have other people speak up on her behalf.
Lyanna nominated Jon, but nobody stepped forward for Sansa. In that situation, neither her nor Jon can really speak up. Ideally Royce should have stepped forward, or Little Finger, but without a hype man or her work being on display, she won't be in people's hearts to be nominated.
I read that scene as her having the chance to speak up, but refusing to do so.
Littlefinger planted the seed in the Godswood, just like he had in Mole's Town, except this time she didn't bite. Sansa sat there in silence for several seconds when she could have spoken up, but instead Lady Mormont finally spoke. Littlefinger's disgust was that Sansa had refused to use that moment to seize power. I think the whole Sansa v. Jon thing is complete misdirection.
Everyone said Jon was dead and that was the end of it last year.
If she wants Winterfell she should have spoke up and made her case. I'm really tired of Sansa's whimpering and crying that she isn't "getting the credit she deserves" when she never opens her mouth or asserts herself. Jon would have supported her, had she stood up and spoken for herself. He said himself that she should be the Lady of Winterfell.
I feel like the writers are just determined to make Jon and Sansa rivals for drama, when it could all be cleared up if Sansa would just fucking talk.
Which she never does.
She wants to prove she's a player of the game, but she's making intrigue and drama where it need not be. Again, if she would open her mouth and assert herself. While I get that, as Ned's trueborn daughter, her claim 'should' be stronger than a bastards, this is a patriarchal society. She is going to have to speak up and fight to be heard, and earn the approval of her Lords.
Not just have it handed it to her.