Set a 6-quart Instant Pot to saute; add olive oil.
In a small bowl, stir together salt, pepper, smoked paprika, and dried thyme. Sprinkle chicken evenly with salt mixture.
When oil mixture is hot, add chicken in batches to Instant Pot. Cook until browned on both sides, about 3 minutes per side. Remove chicken; set aside.
Add mushrooms, onion, and garlic to Instant Pot; saute 4 minutes, stirring occasionally. Add chicken stock and wine to Instant Pot; stir to release browned bits.
Press Cancel to reset Instant Pot.
Pierce each potato with a fork; add potatoes to Instant Pot.
Place top on Instant Pot; twist to seal and lock. Turn Steam Release Valve to “sealing.” Set Instant Pot to cook at High Pressure for 10 minutes.
After cooking is complete, let pressure release naturally (approximately 10 minutes). After that, manually release the pressure by turning the Steam Release Valve to “venting.”
Remove chicken and potatoes from Instant Pot. Place chicken and potatoes on a platter; pour mushroom and juices over both. Garnish with fresh thyme, if desired.