Rinse the jasmine rice under cold water until the water runs clear.
Add the rinsed rice and 1 1/2 cups chicken broth (or water) to the bottom of the Instant Pot; spread into an even layer so the rice is covered.
Season the chicken breasts on both sides with salt, pepper, garlic powder, and ground ginger.
Place the seasoned chicken breasts on top of the rice, then pour 1/4 cup of the teriyaki sauce over the chicken.
Secure the Instant Pot lid and set the valve to sealing. Pressure cook on high for 4 minutes (use 6–8 minutes for very thick chicken breasts).
When the cook time ends, allow a natural pressure release for 10 minutes, then carefully quick-release any remaining pressure and open the lid.
While the chicken cooks, heat the sesame or olive oil in a large skillet over medium-high heat. Add the chopped bell peppers and broccoli and sauté until tender, about 5–7 minutes. Add a few spoonfuls of teriyaki sauce and toss to coat, then remove from heat.
Transfer the chicken to a cutting board and let rest for 5 minutes. Fluff the rice in the Instant Pot with a fork.
Slice the chicken against the grain, then return the sliced chicken and the sautéed vegetables to the pot with the rice and gently combine.
Spoon the teriyaki chicken and rice into bowls. Drizzle additional teriyaki sauce if desired and garnish with sesame seeds, chopped green onion, and Sriracha or crushed red pepper flakes.