Dragon self-insert fiction is this whole world, and honestly, the tropes are what make it. The sheer scale of the power fantasy is one huge one. You see a lot of protagonists waking up as hatchlings and then slowly discovering abilities that make human problems seem trivial. It's a slow, indulgent crawl through hoarding treasure, learning to fly, and dealing with territorial disputes with other magical creatures.
Another big pattern is the 'fish out of water' scenario, but with scales. The main character often retains their human memories and sensibilities, which creates a constant internal conflict. They might try to apply modern logic to a medieval fantasy world, or struggle with instincts urging them to eat the local villagers. That clash between ancient, predatory nature and a more pacifist human mindset drives a lot of the internal monologue.
Isolation is a recurring theme, too. Being a solitary, powerful creature often means a lonely existence. Writers explore this through centuries-long lifespans, outliving human companions, or being hunted as a monster. The stories that hook me are the ones that don't shy away from that melancholy, even amidst all the fire-breathing and castle-smashing. The trope of finding an unlikely friend—a brave knight, a curious mage, or even another reincarnated soul—tends to be the emotional core that balances the power fantasy.