I think the best demonstration of Tears of the Kingdom's misogynistic treatment of Zelda is the comparison between its final battle and the final battle in Breath of the Wild.
While she doesn't appear on the battlefield to fire arrows herself in Breath of the Wild, it is nonetheless inarguable that Zelda consciously and deliberately assists Link in the Dark Beast Ganon fight. Not only does she create and give him the Bow of Light, but she also tells him that the malice covering Ganon's body makes him invulnerable to damage . . . and so she uses her power to draw the malice back to create vulnerable spots for Link to attack.
Link could not have defeated Dark Beast Ganon without Zelda's assistance. He couldn't damage Ganon at all without Zelda pulling the malice back to create vulnerable portions of Ganon's body. And that's not even getting into how it was Zelda who ultimately sealed Ganon once he was weak enough for her to do so, after she had already consciously and deliberately restrained him within the castle for a century.
Now let's look at Tears of the Kingdom. Tears of the Kingdom strips away the bulk of Zelda's agency. Setting aside how the events of the past relegate Rauru as the primary hero, with Zelda only going around to do clean up after Rauru has sealed Ganondorf underground, but Zelda's one big act is to turn herself into a mindless dragon. Yes, she does this to return the Master Sword to Link, and it works; but the moment she swallows that stone, she ceases to both be herself and have any agency at all within the story. Nothing she does as the Light Dragon is because it is something that she, Zelda, as a person, wants to do. And that includes when she shows up to help Link in the final fight.
Because while there is something to be said about subconscious desire, it is simply that: subconscious desire. It's instinct, and instinct doesn't require thought. In fact, instinct is the opposite of thought. She didn't think to herself, Link is in danger and I must help him, because I love both him and Hyrule. She didn't think anything to herself at all. If anything, she as the Light Dragon sensed a Demon Dragon and decided that fucker was in her territory and needed to go. Because Zelda essentially rendered herself an animal. She plays the exact same role in the Demon Dragon battle as Link's horse plays in the Dark Beast Ganon battle, and that is deeply insulting and disrespectful to her as a character, particularly given the role she played in the previous game.
And yes, we do know that it was all subconscious, that she had absolutely no thoughts or awareness of what was going on at all. She tells us this.
Compare this to what Zelda tells Link after Dark Beast Ganon is defeated:
Zelda was able to keep watch over Link. She chose to watch over him as he healed in the Shrine of Resurrection and then journeyed across Hyrule to help her seal Ganon away forever. Versus in Tears of the Kingdom, where she was asleep as a mindless animal. In Breath of the Wild she could utilize agency to choose what she did, and where she paid her attention. In Tears of the Kingdom, she had none and could not.
And it doesn't even end there, because let's compare how she's freed in both games, once the player deals enough damage to get rid of Dark Beast Ganon and the Demon Dragon.
Screenshots really do not do this justice. This sequence, from the moment Zelda bursts out of Dark Beast Ganon's body to the moment she fucking atomizes him (well, seals him, but it looks like she fucking nukes him) lasts for a grand total of 1:36. Which might not seem like much, but it is when it's a game cutscene to finish off the final battle and Link isn't present for any of it. This is 100% Zelda's moment, to the point where it actually mirrors (in the beginning) the moment when Calamity Ganon swallowed her one hundred years ago (not realizing that he was dooming himself when he did, because once she was inside him she was able to restrain him in the castle) only for him to not be able to do it this time. Zelda stands bathed in the golden light of her own power and takes him the fuck out.
And in comparison, here is Zelda in the aftermath of the Demon Dragon battle:
Zelda doesn't return to her mortal body because of anything she thinks, wants, or does. Instead, Link, Rauru, and Sonia do that for her. And she's completely unconscious for everything in the following sequence; Link has to save her as she falls out of the sky, and doubtless would have died if he hadn't. Whereas she had full agency to shut Dark Beast Ganon down in the climax of Breath of the Wild, she has absolutely no agency at all in the climax of Tears of the Kingdom.
And don't get me wrong, the ending sequence of Tears of the Kingdom is beautiful. That last screenshot there is gorgeous. And just like Breath of the Wild paralleled the moment Calamity Ganon swallowed her (and then she restrained him) in the final battle, this ending sequence parallels Link trying and failing to catch her at the start of the game. I, too, was moved by Patricia Summerset's performance as Zelda realizes what Link has done for her (it was some of her best acting as Zelda; you could hear the tears in her voice), and as a Zelink shipper, the "felt a warm, loving embrace" line really gets me. I get all of that.
But we can't ignore the vast difference in Zelda's role in these two games and, specifically in this case, their climaxes. No, female characters don't have to fight and be physically powerful to be strong characters. And in fact, it's easily argued that Zelda isn't a fighter. Link is the one who fires the arrows from the Bow of Light, after all; he's the one that deals all physical damage to Ganon. But setting aside how Zelda assisted him with restraining the malice and then did the final sealing, what I'm highlighting here is less her literal actions and more the fact that she was able to make them at all.
Character agency is their ability to make decisions and take actions within the narrative. In Breath of the Wild, Zelda has extraordinary agency within the narrative. It's her story. Even in the flashbacks, when she was drowning under the pressure of her responsibilities and Rhoam restricted the actions she was allowed to take (i.e. banning her from working on the ancient Sheikah tech), she still made her own decisions and took actions independently within the narrative. She routinely ditched Link before she warmed up to him. In the voice memories, it's made explicit that she spends little time in her bedroom because she spends all of her time in her lab instead. She's the one who sends Link to the Shrine of Resurrection, who returns the Master Sword to Korok Forest, and who finally makes her way to the castle and holds Calamity Ganon captive for one hundred straight years, while being conscious literally the entire time.
Tears of the Kingdom is the exact opposite. She's yeeted to the past against her will. Rauru makes all of the major decisions regarding how to handle Ganondorf, while Zelda passively makes suggestions. (The one time we see Zelda perhaps concoct a plan, it's one she made with Sonia that resulted in Sonia's death.) When Rauru sacrifices himself, Zelda goes and asks the past sages to have their descendants help Link in the future, and then turns herself into a mindless dragon as her one big act in this game, thus completely destroying her sense of self and any chance of agency she may have had in the rest of the plot.
There is a lot to hate in Tears of the Kingdom, and a lot that I, personally, hate. And let it be known that I have always been a hater; my "totk critical" tag started in the very first month the game was released, and while there's not too much in there, there's still enough to show that I've loathed the story of this game for years. And considering I play Zelda games for the story, my hating the story means that my hatred for this game runs deep.
But while there is a lot to hate about the story in Tears of the Kingdom, this is the aspect that I hate the most. Breath of the Wild, for all the ways in which it can be criticized, handled Zelda, as a character, phenomenally. Although the game tells you over and over that you have to save Zelda, and keeps harping about how Link is the hero of Hyrule (and Zelda's low self-esteem has her constantly talking about how he is Hyrule's last hope, and how he saved everyone, etc etc, completely downplaying her own accomplishments here), not only is Zelda the true protagonist of this story, but she is also, in my opinion, the most heroic character in it.
Tears of the Kingdom saw that, and then decided to do the complete opposite. Zelda was damseled once again, inarguably and so much harder than Breath of the Wild could ever dream of. Her role as the one who seals Ganon was handed over to Rauru, despite how that completely breaks the series lore (he should not have Hylia's power, Sonia should have had it, it makes no goddamn sense and it makes me so mad). Her agency is ripped away from her, and I can't see any reason for it other than misogyny.
I'm not saying that the writers sat down and said, "Man, we really hate women and treated Zelda way too well last time, let's treat her extra badly this time to make up for it." In fact, I would be willing to make a monetary bet that they think they did okay by Zelda in this game. The awful thing about misogyny is that it is so baked into the patriarchal fabric of our society that most people don't realize when they're participating in it. It sucks, but it's reality. And with it being reality, I can't see Zelda's treatment as anything but misogynistic in Tears of the Kingdom, particularly with how she was treated in Breath of the Wild. And the final battles between the two games demonstrate that better than almost anything else could.