Toss together chicken, salsa, honey, chipotle chiles, salt, and garlic powder using tongs in a programmable pressure multicooker, such as Instant Pot. (Times, instructions, and settings may vary according to cooker brand or model.) Cover with lid; lock in place. Turn steam release handle to SEALING position. Select MANUAL/PRESSURE COOK setting. Select HIGH pressure for 8 minutes. (It will take 12 to 14 minutes for cooker to come up to pressure before cooking begins.)
Carefully turn steam release handle to VENTING position; let steam fully escape (float valve will drop). This will take 1 to 2 minutes. Remove lid.
Transfer chicken to a bowl, leaving chile mixture in cooker.
Select SAUTÉ setting on cooker. Select HIGH temperature setting; bring chile mixture to a boil. Boil, stirring occasionally, until sauce thickens, about 15 minutes. Press CANCEL.
While chile mixture thickens, shred chicken using 2 forks.
Return shredded chicken to cooker; stir to coat in sauce. Add additional salt to taste, stirring to combine.
Serve with warmed tortillas and desired toppings.
