Set your Instant Pot to sauté mode and add a splash of oil. When hot, add chopped onions, carrots, and celery, sautéing until they soften slightly and the mixture smells fragrant, about 5 minutes.
Add the chicken breasts on top of the sautéed vegetables, then pour in the broth. Sprinkle with dried thyme and season with salt and pepper to taste. Seal the lid securely.
Cook on high pressure for 10 minutes, then let the pressure release naturally for about 10 minutes before opening the lid. The chicken should be cooked through and tender.
Carefully open the lid, remove the chicken breasts, and shred them with two forks. Return the shredded chicken to the pot.
If using noodles or rice, add them now and set the Instant Pot to sauté. Cook until noodles are tender or rice is fluffy, about 5 minutes, stirring occasionally.
Squeeze fresh lemon juice into the soup for brightness, then taste and adjust seasoning if needed.
Sprinkle chopped parsley over the soup for a fresh herbaceous note, then give it a final stir.
Serve hot, ladling the soup into bowls, and enjoy the comforting warmth and tender shredded chicken in every spoonful.