My barebones idea of a framework for how it would work:
Stay Single: I'll just stick with my original framework.
Anko Framework: Due to being an extra, the MC will be assigned to her as a pair. Due to MC not having the same bias against her as most of the village, she eventually warms up to the MC. She will flirt with the MC jokingly, eventually the MC will respond in a positive way making Anko realize she had already developed feelings for the MC. Probably something like Anko teasingly saying "love ya" with MC thoughtless replying "I love you too" before one of them running away in embarrassment after realizing what was said .With help (not sure how yet) they manage to remove the curse mark containing Orochimaru's soul
Tayuya Framework: Before the attack on the leaf, she was scouting the village where she continued to run into MC and falls in love with her without realizing. While escaping after the attack on the leaf, she gets distracted for a moment by the MC about to be killed by a sand shinobi and saves her without thinking, leading to her getting left behind and due to the confusion caused by her saving the MC they both get locked up. While locked away she gets the opportunity to interact with MC and realizes that she had already fallen in love with her. Similar to how it would go with Anko, with help (still not sure how) they manage to remove the curse mark containing Orochimaru's soul. Of course, she won't even be introduced until later.
Ayame Framework : already established that due to Naruto's Ramen addiction they get ramen once a week. Eventually they developed mutual feelings for each other, but due to the 5 year age gap she will initially quash those feelings and be opposed to a relationship. Eventually, MC will convince her it wasn't just a childhood crush, and that MC's feeling are sincere, leading to a relationship
Tenten Framework: while practicing with needles as a throwing weapon, they meet at the training ground. Tenten gives her advice and helps her get better with her weapons. Also, due to being inspired by Tenten she starts using shuriken more than needles, and later evens swaps out her wakizashi for a collapsible Bo (i.e. a folding staff)
Two things that should be mentioned if choosing Tsunade: First, Hiruzen will almost certainly have to die (He might die anyway, but that's something I'm still considering.) Second, it will not be a happy story.
Tsunade Framework: Sakuya will go with Jiraiya and Naruto to look for her. Things will pretty much go like canon up to when orochimaru appear. Shizune will get severly injured, and after the battle it's clear that Tsunade will be the only one that can save her but due to her fear of blood she can't. MC will say something about ending her misery then stab down with a fake knife she picked up at some point, only to be blocked by tsunade who then procceeds to heal her, realizing after that her own hand is uninjured. Sakuya convinces Tsunade to teach her medical ninjutsu, and over time they grow close. The day before Tsunade is sworn in as hokage, she is assassinated. Sakuya tracks down the killer and finds out it was some sort of coordination by Danzo. Sakuya goes to Kakashi for advice, but he refuses to acknowledge that she could have determined the killer so quickly when even the Anbu had yet to figure it out. Having been spurned by him, her grief causes her subconsious limiters to vanish allowing her use her powers more than ever before which she uses to she stops time and kill literally every member of root other than Danzo, resuming it to tell him why he will die before proceeding to completely erase his existence by accelerating his time to the point he turns to ash, not even giving him the chance to use Izanagi. Having realized that she could possibly reverse Tsunades time to bring her back to life, she rushes back but due to some scheme by Danzo she had already been cremated and her ashes scattered and thus unrecoverable. MC goes effectively insane and decides to say fuck canon, going rogue and in order to take over the Akatsuki she assassinates pain by wiping out the rain village from existence along with everyone in it, basically putting her as a kill on sight. Yada Yada, succeeds in takeing it over, yada yada She declares fourth shinobi war except instead of wanting peace she quite literally decides that no one deserves to live in a world that took the person she loves yada yada she either succeeds and proceeds to live on a lifeless world in mourning for all time or Naruto kills her, dunno which and that would be hundreds of chapters away so I don't even have to think about, Especially since I'm sure this won't be chosen. I only wrote this much because this was kind of a fun framework to write out.
For the following I may go with the second place because they could be difficult to work in
Hyuga Hanabi Framework: She follows Hinata to MC/Naruto's place at some point and Meets the MC. She is initially extremely jealous of her due to Hinata referring to her as sister dearest (maybe I should swap that for Sakuya nee-sama or Onee-sama. depending on how I have Naruto refer to her I'll consider it. I guess over time she starts to refer to Sakuya as onee-sama and flowers of yuri bloom or something
Sakura Framework: they meet at the academy and due to both being top students, Sakura asks her if she would be willing to study together. They spend time together, and MC convinces Sakura of the importance of knowing how to actually fight making her not be complete baggage for team 7. eventually they develop feelings for each other.
I may also use this framework if MC is not on team 7 to make Sakura less baggage, but instead of developing a bond of love they instead develop a strong bond of friendship
Ino Framework: they meet at the academy and due to struggling with flower arrangment, asks Ino for help. This leads to them spending time together and eventually developing feelings for each other.
Inuzuka Hana Framework: MC will start to volunteer to help out at the Inuzuka Clan compound whenever she get's the chance. MC will learn medical ninjutsu, and at some point one of her dogs gets severely injured and MC manages to save them, leading to them getting close. I'm not quite sure how to make it work.
Almost certainly won't go with the following without some sort of spark of inspiration:
Temari: she canonically was at the same Chunin exams as team 7, so I guess they would meet there
Kurotsuchi: she canonically was at the same Chunin exams as team 7, so I guess they would meet there
Uzumaki Karin: I honestly have no clue how to do this one
TONTON: this is a joke, if it somehow wins while I will have to go with second place I suppose I can add in some friendship developing that causes Sakuya to like pigs more than dogs. If this and Tsunade are in the first two places, and should I go with MC wiping everyone out, she'll spare tonton and it will be a lifeless world with her and an immortal pig (three cheers for the power of friendship).
Mei Terumi: it's not happening, I just think she's cool so I added her in because why not.
MIGHT GUY Framework: really? At best I could do an omake chapter, but I truly just put this here because as everyone knows, Might Guy is a sexless organism that reproduces through mitosis so it would be neither Hetero nor Yuri. I guess it would go something something like they meet while she's training, something something, they get close due to training together, something something, magical genderbending (gender granting? idk) happens to him, something something, feelings develop, something something, they get together, something something, they run of towards the sunset shouting youth while Lee says "congratulations Guy-sensei" through tears of joy, something something, the end.
TONTON!!!
Sakuya and the immortal pig live in a destroyed world until a large space opens before their eyes.
They look inside to find another world, and without much thought, both enter it... And everything changes when they meet a certain someone.
Sakuya knows who they were and, without much thought, decided this was the most interesting scenario: becoming the maid of a vampire. Tonton didn't understand but stayed with her.
After many years, Tonton had become a youkai girl, and the affection Sakuya had for her slowly became something more. In a few moments, their lady will transport this scarlet mansion they cleaned and protected to a new place full of possibilities. Gensokyo.
This is the beginning of their story in the land of fantasy.
...
WHY DID I WRITE AN FANFIC ABOUT THIS?
Now, as tempted as I was to vote for Guy…
Well, I'm simply too afraid, too weak to bear the consequences of my actions. So I picked some others.
I hope you don't just outright forget Hanabi exists like almost every other fanfic ever.
(I must note that, at the time of editing this comment, I am still the only person who voted for Sakura. Not because I liked her character, but because I really- and I mean REALLY- wanted to see Sasuke die a sad, miserable, lonely death. I'm still pleasantly surprised by Hanabi being in the lead though.)