My favorite thing about this fight is that when Aang takes himself out of the Avatar State, his fire, water, and earth bending all go away, and he's left with just air. he's surrounded by his element, and standing up for what his people believed in, saying that what they believed had strength and had value, and refusing to go against it and kill someone.

15:23 "Come on out, avatar! You can't hide in there forever!"

Did nobody else see Aang hiding into a ball, while the world around him is on fire, as being at least slightly reflective of what he did 100 years ago?

Aang's decision to spare Ozai's life probably is what led to building a lasting peace.  He might not have realized it consciously at the time he decided to spare him, but by doing so he prevented turning Ozai into a martyr.

I think it's important to note: every time Aang dropped out of his Avatar state, he always fainted. This fight is the only time he doesn't do that, he is rigid on his feet because he so strongly believes he shouldn't kill Ozai

I think an argument can be made that Aang's insistence to his belief—that he shouldn't have to kill the fire lord in order to stop him—is the very thing that earns him the technique he uses to win the fight.
First, Aang refuses to accept the alternative, to the point where it attracts the Lion Turtle to him—creatures which have been foreshadowed throughout the show, yet which never made a living or spirit appearance by that point. Aang even asks past Avatars of all four elements for their wisdom or guidance, and none of them have a satisfactory answer.
Second, and here's the thing: the show presents the most transcendent beings to have an understanding of time that surpasses the linear, as a result of their connection to their highest true self. That's not Avatar stuff, as Guru Pathik teaching the chakras reveals, and it's first established in The Swamp, when Aang sees a vision of Toph who he has yet to meet. The Lion Turtle did not "coincidentally" come to Aang on Ember Island and give him a ride to the EXACT spot of land that Ozai would later start his attack at. The Lion Turtle knew because it is more transcendent (enlightened?) than even the previous Avatars combined. But wait, there's more! The Lion Turtle has seemingly not deemed any of the previous Avatars worthy of the knowledge of energy bending either, or anyone else for that matter—no characters throughout the show express any indication they think this could even be a thing. MAYBE Ran and Shaw know, but they obviously did not divulge that information. The Lion Turtle came out of hiding because he deemed Aang worthy of knowing this ability, which—hey, let's be real honest here—is a super dangerous power to bestow on anyone. Hence: "The true mind can weather all lies and illusions without being lost. The true heart can touch the poison of hatred without being harmed." + "To bend another’s energy, your own spirit must be unbendable or you will be corrupted and destroyed."
Aang earned the knowledge of energybending by demonstrating his spirit to be unbendable when it comes to valuing life. And that is the highest value to be unbendable about.

Beginning of the fight: a 12 year old boy is going up against the most powerful man in the world. End of the fight: a man fighting for his life against a god.

I'll never get tired of "why avatar was so perfect" videos

Man I had totally forgotten that was Mark Hamill as Ozai.

"That's why characters were restrained to remove their bending."
*Shows a picture of Bumi, a character that bent earth with his face

Hi, random physics thing:
I would also like to point out how Aang made the rocks smaller when he entered the Avatar State. By decreasing the volume of the rocks without changing the mass present, he increased the density of those rocks by a significant amount.
That means if Ozai got hit by even one of those rocks with enough speed, he would have been torn in half.
Thank you for coming to my Ted Talk.

A minor note on the Lion Turtle: you don't really think it was a coincidence that Aang woke up on one, do you? Despite being in the physical world, his scent was so thoroughly erased that June's tracker animal thing was convinced he didn't exist. That Lion Turtle came for Aang specifically, and didn't want anyone else to interrupt.

Now, I do think they could have foreshadowed the Lion Turtles better. The opening sequence of the show (although his airbending skills are good, he has a long way to go before he's ready to save anyone) has Aang riding an air scooter face first into a statue of a Lion Turtle, he is impressed by a portrait of one in the Spirit Library, and a few mansions have Lion Turtle door knockers, but you have to pay very close attention to notice that, and even then you'd have no way to know what it means.

One more quick note about Aang's initial attack taking down the Firelord's ship: Where Ozai's attack is all brute force, Aang's is targeted. He doesn't try to blast Ozai with fire to get him to stop blasting fire; he attacks his ship with precise rock throws and concentrated fire. This is as much a reflection of who Aang is as Ozai's opening move is representative of Ozai's character. Aang doesn't want to damage more than what is necessary, doesn't want to kill Ozai, and uses his mind to come up with alternative solutions that emphasize surprise and quick thinking rather than brute force. You can tell who each of these characters are before either open their mouths, even if you've never seen the show before. This also foreshadows the final resolution of the conflict, where Aang doesn't kill Ozai but instead takes his bending, finding another solution that doesn't involve him just brute forcing his way to victory.

I just want to clarify that Aang didn’t just happen to wake up on a lion turtle. The past episodes beforehand showed aang’s inner turmoil with the idea of taking the fire lord’s life. I believe that the lion turtle, the holders of bending, heard aang’s spiritual call for help and came to him. As we could see, Aang’s spiritual side responded to the presence of the lion turtle and met him in the ocean.

The lion turtles only show up in a desperate time of need; therefore it was premeditated. I don’t think you can call the climax a coincidental win, because in the world of avatar, the spiritual side is just as important as the physical side

"Firelord Ozai, you and your forefathers have devastated the balance of this world, and now you shall pay the ultimate price!" The delivery of that line with all the Avatars speaking through Aang was so badass

I also love that you can actually see the full potential destructive power of airbending. Aang over the course of ATLA almost never uses his airbending agressively, mostly just to avoid getting hit himself or pushing over opponents. Seeing a strong and concentrated gust of wind decimate a stone pillar was one of the highlights for me watching this scene for the first time.

18:38 Gotta disagree with that. That isn't a coincidental tap on the back. Eastern mysticism doesn't even acknowledge the concept of coincidence. The avatar state is entirely the creation of Ozai. It was his daughter acting on his wishes that almost killed Aang and gave him that scar. What we're seeing is the direct reaction of the Firelord's unawarranted violence towards the world coming back to bite him.

I'm actually seeing stuff I've never noticed before. For example:
1. When Ozai clapped his hands when thanking the universe for providing the Avatar to him on a metaphorical silver platter, that clap was actually a brief, genuine, "give thanks for the meal" gesture in some Eastern cultures, akin to (and IIRC inspired by) the prayer gesture in Christian cultures. And as opposed to other Large Ham hand gestures that other loud bully world leaders do, or that Ozai had done in other parts of the scene, that seems to have been an intentional decision, noted by the fact that that small gesture had a disproportionately loud sound effect.
2. When Aang stopped the Avatar State from dealing the killing blow, he didn't stop it all at once. He only stopped the arm that was dealing the killing blow, after which the State shut itself off. This suggests that Aang was fighting an internal struggle against the Avatar State that we only saw the end of, where the Avatar State eventually relented after he mustered up enough power to stop that one attack that was moments from going through (slightly downplayed by the comedy of the water and pebbles landing on Ozai's face.
3. When Ozai first shoots fire during the comet, even he seems surprised by how much and how powerful it is. But by the moment in which he produces that concentrated stream to blast the cornered Aang, he's gotten such a complete handle on his newfound power, from internal learning over the course of the fight, that he's able to turn it from (yellow) wild lightning, instantly to a compressed, far more powerful concussive stream. We've already seen at several points in this fight and in the series that compressed elements tend to carry more power behind them, here he did both compression and a phase change, of what was possibly going to be the most powerful stream of fire seen in the series so far.

In a way Aang did try to seek out the lion turtle, but not specifically. He ran away to search for another way to defeat Ozai without killing him, and his search lead him to the turtle. So it wasn't explicitly a search for the lion turtle, but a search for an answer which he ultimately received by learning energy bending from it

Aang didn't get energybending through happenstance. We have two episodes of Aang doing some serious introspection, going on a spiritual journey that also follows narrative structure, and only when he accepts the wisdom of his past lives does the Lion Turtle give him the insight he needs in order to energybend. Buddhist fans have pointed out the similarities between Aang's journey in the finale and Buddhist parables. And even after the Lion Turtle teaches energybending to Aang, he still risks his life by trying to use it. There are high stakes, and the show makes this clear. This solution wasn't just handed to Aang. It's not a deus ex machina.

I think the fact that you overlooked this is obvious given the line of Ozai's that you didn't discuss. "You are weak, just like the rest of your people. They did not deserve to exist in this world, in my world!" Despite it being in the show's title, we in the fandom don't talk enough about how Aang is the last airbender.  This fight is not just the avatar vs. the firelord. It's the sole survivor of a genocide against the imperial power that destroyed his people. Throughout the show, Aang has been forced to give up parts of his identity as an Air Nomad. He was forced to accept the disfigurement of the Northern Air Temple, was separated from Appa, burned his glider, hid his tattoos. And finally, he's faced with giving up his regard for the sanctity of life. If he abandons this core value of his people by killing the firelord, the airbenders truly will no longer exist in the world. Aang using the spiritual strength he has honed throughout the series in order to both follow his people's teachings and save the world defeats Ozai not just physically, but spiritually as well. Ozai's worldview of might makes right has been overturned by Aang's practice of peace. Aang using energybending strengthens the narrative, not weakens it.

Admittedly this is my own interpretation, but I’ve always seen Aang’s lucky-chakra-point-release-on-a-convenient-rock as a contrast to Ozai’s claim that the universe had delivered Aang to him in an act of “providence”.