Movie starts out with a young Bowser, outcast and bitter, wanting more in his life. While wandering through the Mushroom Kingdom, he happens upon an item that grants the magical power of transformation. He decides to use this for personal gain. Essentially becoming Mystique (X-men) he goes through a long arc gaining influence throughout the kingdom and eventually claims the crown. As his influence grows, so does his lust for even more power. He isn’t happy just being on the throne, he wants a complete dictatorship.
One of the loyal regional governors, Donkey Kong, shares a story about his past, when his father discovered a portal to the human world and lured a human here to rescue his girl (Daisy). This gives Bowser an idea.
Bowser visits the portal to the human world, transforms into Peach and lures Mario into the Mushroom Kingdom to chase her. Bowser’s goal is to use Mario as a “terrorist” to fearmonger the citizens of the Mushroom Kingdom. Same idea as what Palpatine did in Star Wars. With Mario wreaking havoc on all the creatures, they would accept Bowser’s request to become the Supreme Chancellor, vesting in him complete power to protect them from this new threat.
As Peach, he leads Mario through the world, tricking him into killing creatures to “save her from them”. Then, as Bowser, he shares the details of these adventures with the citizens, showing what a destructive force Mario is. The more creatures Mario kills, the more his narrative is believed around the kingdom. The more they believe it, the more they attack him and the more Mario believes that he must fight in self-defense. Thus the arms race ramps up to a climactic reveal.
In front of the castle, Bowser is revealed to be the same person as Peach. He gets caught in the middle of using the transformation item when it gets snatched away from him. He ends up permanently stuck in a halfway state between Bowser and Peach (Bowsette) while also seeing the transformation item destroyed.
Bowser expects that Mario will realize the deception and be angry. But the opposite happens. Mario says that if this is the person he’s been adventuring with all along, then this is the person he loves. He says that Bowsette is hot AF and he wants to be with her, whoever she is.
The citizens of the Mushroom Kingdom see Bowser’s deception and realize that Mario was not the bad guy all along. They lock Bowsette up in the dungeon of the castle and let Mario visit her as he sees fit.
The movie ends there, setting up a potential sequel where Bowsette will try to use her charms to manipulate Mario into freeing her so she can regain her power.