For me, one of the most cryptic Naruto scenes was the moment when Tsunade woke Sasuke up from his Tsukuyomi-induced coma and then Sakura hugs Sasuke. This was a very challenging scene for me to decipher. I remember clearly the first time I saw it, because even back then I knew this scene was significant. Naruto's reaction to the hug perplexed me because I didn't fully know what it meant, only that the author was telling me something important with that scene, I just didn't yet know what. Years later after reading many analyses of the series and its characters, I feel confident I understand the point of this scene. It's an important Team 7 scene representing the shift in the relationships between Sasuke, Sakura, and Naruto, and it displays how much Naruto and Sakura both have grown and matured.
I've heard criticism that SasuSaku fans look too deeply into this hospital hug scene and desperately use it to advocate the ship as an affectionate moment between Sasuke and Sakura, when to anti-SasuSaku fans it merely looks like Sasuke woke up from a coma and is too traumatized and tired to resist Sakura's display of affection, or even to react at all. Given only the picture of the hug and vague knowledge of the scenario, I would agree with antis on that. In fact my original interpretation of the scene was similar; Sasuke looked totally traumatized and unresponsive to his surroundings and he had a 'dead on the inside' look if I ever saw one and at a cursory glance Sakura's hug seemed a bit irrelevant to what Sasuke was going through.
However.
What these criticisms don't account for is context. There's far more occurring in this scene than just Sasuke's dead-on-the-inside expression and Sakura's hug.
Certainly Sasuke's reaction seems subdued, as if he's too dazed and traumatized to register much. Well, I say that, but Sasuke is visibly looking at Sakura. When he woke up, he seemed dazed and distracted, but when Sakura hugged him, he's definitely looking at her. It means that as dazed and out-of-it as he was, her presence nonetheless captured his attention and focus, so he's no longer staring blankly out into space, but actively looking at her.
There is also the "thoughtful ellipsis". The thoughtful ellipses is something Kishimoto uses frequently uses throughout Naruto to convey deep emotion without dialogue. It means that a character is having a significant, thoughtful emotional response to what is happening around them even though they don't say a word. Thus we see that Sasuke is responsive to Sakura's hug and thinking about it. His expression is not a blank slate but a meaningful one.
There are other details cluing readers into what is going on, coming from Naruto and Tsunade.
Even though Tsunade knows nothing about Sakura, she notes right away that Sakura's concern for Sasuke is genuine and diligent. Sakura has visited Sasuke every day at the hospital, always bringing him a flower for his hospital room and barely leaving his side until he got better (after all, it's telling that she was already there when Naruto arrived with Tsunade). Noticeably it's Sakura, and not Ino, who is by Sasuke's side, which on Sakura's end emphasizes a higher sense of loyalty, friendship, and involvement with Sasuke that goes beyond a mere fangirl's crush.
Upon her arrival, Tsunade immediately takes note of this upon entering the room. Via Tsunade's perspective we note the Fifth Hokage's sympathy for this girl who has spent the past month or so worrying for her friend, awaiting his awakening. Tsunade is impressed and surprised that the girl has been so diligent with visiting Sasuke and staying by his side as much as possible until he recovered (which is what a good and loyal friend would do).
Noticeably Tsunade is assessing Sakura's reaction as she heals Sasuke rather than watching her patient as she heals him. As Tsunade works her healing magic, Sakura is visibly tense, torn up with anxiety and worry (the reaction I'd expect from a concerned friend). Sakura's greeting to Sasuke is full of tearful relief, whereas Naruto's nonchalant, carefree greeting made it appear like nothing particularly worrisome had happened to Sasuke (when Sasuke had just been horrifically abused and tortured and had been knocked into a coma that lasted for a month).
When Sasuke awakens, Sakura throws her arms around Sasuke and tears pour down her face.
Meanwhile, Naruto begins to greet Sasuke up with a casual greeting, but notably soon trails off and falls silent. Since this is an analysis about SasuSaku, I'm not going to go into Naruto's character growth too in-depth other than to say that this moment represents his increase in maturity. Naruto starts out as a usual chipper self, until Sakura hugs Sasuke and starts sobbing. Naruto doesn't seem bothered by Sakura's distressed and tearful reaction as she throws her arms around Sasuke and her body shakes with sobs. But when Naruto looks at Sasuke's expression, Naruto immediately becomes somber and looks unhappy.
Naruto notices something in Sasuke's expression that causes him to pause. Maybe fans might try to deny it has anything to do with Sasuke caring about Sakura, perhaps arguing that it's just Naruto being stricken by how traumatized and dead on the inside Sasuke looked, but that can't be it. Naruto already saw Sasuke's dead-eyed look when Sasuke initially sat up from his bed, yet Naruto wasn't immediately shocked by how awful Sasuke looked. Additionally, Naruto gently smiles after his initial somber reaction (smiling isn't something I expect Naruto to do if he's aware how bad of shape Sasuke is in mentally, so there clearly must be something else going on).
Naruto quickly reads the mood, showing sensitivity and adeptness at reading people's emotions, more so than he has previously. He stops being oblivious to his two teammates' feelings like he has been regularly until this point. Before, Naruto had childishly vied for Sakura's attention and affection, criticizing her for liking Sasuke and trying to redirect Sakura's crush on Sasuke to himself. But this moment is the first time that Naruto sees that Sakura's love for Sasuke is real and built upon a genuine concern and care and love, not a superficial crush like Naruto had thought.
Notice how Naruto can only see Sasuke's face during this moment? Naruto can't read Sakura's expression because he can't even see it. Naruto can read only Sasuke's expression, and what Naruto sees is that Sasuke does accept Sakura's love and feelings. Naruto had assumed that Sasuke didn't care about Sakura romantically either, but now Naruto sees that isn't the case: for the first time Naruto sees that Sasuke does love Sakura. Naruto hadn't realized that Sasuke cared about Sakura that much before; I dare say Naruto hadn't realized that Sasuke needed Sakura's love and friendship until this moment. Before, Naruto had always thought he stood a chance with Sakura. But now Naruto knows that Sasuke cares about Sakura too and accepts her affections. It's not a one-sided crush like Naruto thought; an actual relationship had formed between Sasuke and Sakura at some point, and Naruto had been completely oblivious and unaware of it. But now, Naruto sees the genuine tender love between them.
And so, Naruto initially looks startled, then serious and upset, and then he smiles. It's a nice character moment for Naruto, displaying how far Naruto has grown and matured as a person during his time of Team 7. At the start of the series Naruto had only cared about getting everyone's respect and admiration and winning Sakura's heart. Now more mature, Naruto doesn't care about getting Sakura to love him instead of Sasuke anymore. Of course losing Sakura to Sasuke is a severe personal blow to Naruto, but what Naruto really wants is for his teammates to be happy. If Sakura makes Sasuke happy and vice versa, then their happiness is enough to make Naruto happy and he's content with that. So Naruto smiles, happy for his teammates because he sees that they give each other something special that Naruto doesn't want to take away from them.
There are a few other details supporting this.
In the anime version of this scene, the camera pans out, creating distance between Naruto and Sasuke & Sakura (and it's even done with a white background, which in anime usually indicates something significant). It's a symbolic way of showing that Naruto is realizing that at some point, somehow without him noticing, Sasuke and Sakura had developed a special bond between them that he knows he could never touch or fully share in (thus the reason for the distance created between him and them, because Sasuke and Sakura are now coupled together in a special bond between them and only between them, and it's a bond that Naruto knows that he can never fully be a part of).
In the manga version of the scene, Naruto has inner dialogue (unfortunately the anime omitted his inner dialogue), musing that "Sasuke...you..." Naruto doesn't finish his sentence, but his incomplete dialogue shows Naruto realizing that Sasuke does have feelings for Sakura and accepts her affection. Thus why Naruto looks initially serious and somber, but after a moment's pause, he smiles gently to himself. Because despite how heartbroken he is over losing Sakura, Naruto is happy for his teammates.
This is why Naruto chose to leave the room to give his teammates privacy.
In case you want to argue that Naruto is a naïve kid who doesn't know what love is and that Naruto is misreading the dynamic between Sasuke and Sakura: it may be true that due to his lonely childhood Naruto is somewhat inexperienced with relationships (although literally the point of this scene is to show how Naruto is maturing past that inexperience, but whatever), but Tsunade sure isn't. Tsunade is a mature, 50-year-old adult who wasn't born yesterday. Like Naruto, she observes Sasuke's and Sakura's interaction to have romantic undertones, which is why she's impressed with Naruto's maturity in observing the dynamic and giving the two time alone. Tsunade notes that Naruto does have a sensitive side and she's impressed that he is able to pick up on subtle nuances of a relationship and know when he's a third wheel and respond appropriately by giving his teammates privacy instead of interjecting himself where he's not wanted.
At this point, I don't know that I'd describe Sasuke and Sakura's bond as romantic quite yet, but their relationship appears to be in a fluid stage somewhere in-between friendship and romance, and this scene marks the shift - or at least marks that Naruto has finally noticed the shift in his two friends' relationship.