Set your Instant Pot to the 'Sauté' mode and add the olive oil. Once hot, add the diced onion and cook until it becomes translucent, about 3-4 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the sliced carrots and celery, stirring to combine. Sauté for another 3 minutes.
Sprinkle in the dried thyme, dried parsley, black pepper, and salt. Stir everything together.
Pour in the chicken broth and place the chicken breasts into the pot.
Close the lid of the Instant Pot, making sure the steam release valve is sealed. Set it to 'Manual' mode and cook on high pressure for 10 minutes.
Once cooking is complete, allow the pressure to release naturally for 5 minutes, then carefully perform a quick release for any remaining pressure.
Remove the cooked chicken breasts from the pot, shred them using two forks, and return the shredded chicken to the soup.
Add the egg noodles to the pot and stir. Close the lid again and cook on 'Soup' mode for an additional 4 minutes.
Once done, perform a quick release again. Stir in fresh spinach if using, and allow it to wilt for a minute before serving. Adjust seasoning if necessary and finish with a squeeze of lemon juice if desired.