Turn Instant Pot on to SAUTE mode. When Instant Pot says "Hot" heat olive oil and sauté onions until translucent. Then press CANCEL button to end saute mode.
Add broth to the pot and deglaze the bottom of the pan by gently scraping the flavorful brown bits off the bottom of the pan. There is no need to discard the brown bits. Rinse brown rice and add it to the pot. Stir in carrots and mushrooms.
Arrange chicken breasts on top of veggies and rice; season with salt and pepper.
Add cream of chicken soup to the top of the chicken and add sprigs of thyme. *Do not stir in the cream of chicken!
Secure lid on Instant Pot, and turn nozzle to SEALING.
Cook on MANUAL high pressure setting for 25 minutes. Then Quick Release. Be careful not burn your hand on the hot steam!
Once steam has released, open Instant Pot lid and stir to shred the chicken and combine with rice and veggies.