Place the flour, 1 teaspoon salt, and 1 teaspoon of the paprika in a zip-top plastic bag and shake to combine. Trim the excess fat from the chicken thighs, add them to the bag and shake until coated with the flour mixture. Set aside.
Press the "sauté" button on the Instant Pot and add the butter. As soon as the butter melts, add the celery and onion. Season with salt and pepper, add the remaining teaspoon of paprika and sauté until lightly browned, 4 to 5 minutes.
Stir in 1 cup of the chicken broth and scrape up any browned bits from the bottom of the pan with a spatula. Add the chicken thighs in a single layer, turning them once or twice to coat them in the broth mixture.
Cancel the "sauté" function and lock the cover onto the Instant Pot. Use the "manual" function to set the Instant Pot to cook for 5 minutes at high pressure. Once the time is up, allow the pressure to release naturally, then transfer the chicken to a plate and cover with aluminum foil to keep warm.
Add the remaining cup of broth the the Instant Pot and stir in the noodles. Lock the cover on and use the "manual" function to set the pot to cook for 4 minutes at high pressure. When the time is up, let the pressure release naturally for 2 minutes, then open the valve to release the remaining pressure quickly.
To finish the dish, press the sauté button on the Instant Pot and return the chicken to the pot. Cook just long enough to heat through, about 2 minutes.
Using a slotted spoon, transfer the noodles and chicken to to a serving platter and set aside. Add the sour cream and tomato paste to the sauce and whisk until smooth. Spoon the sauce over the chicken and noodles and serve immediately.