Add the chicken breasts, salsa verde, diced jalapeño, chili powder, kosher salt, and black pepper to the Instant Pot insert. Do not add the Greek yogurt yet.
Secure the lid and make sure the pressure valve is set to sealing. Select Manual/High Pressure and set the timer for 15 minutes.
When the cook time ends, allow a natural pressure release for 5 minutes, then carefully perform a quick release to vent any remaining steam and open the lid.
Use tongs or a slotted spoon to remove the chicken to a cutting board or bowl and shred with two forks.
Return the shredded chicken to the Instant Pot, add the plain Greek yogurt, and stir until the mixture is smooth and combined.
Switch the Instant Pot to Sauté, bring the mixture to a gentle simmer, and cook for about 5 minutes to heat through and thicken slightly, stirring occasionally.
Serve hot.
