Heat Instant Pot to "Sauté." Add oil, celery, onion, salt and pepper. Cook, stirring frequently, until onions are translucent, 3 to 4 minutes.
Add broth, water, and chicken. Secure lid and turn valve to "seal." Set Instant Pot on Pressure Cook (or Manual, high pressure) for 11 minutes. Quick release pressure when done cooking and carefully remove lid.
Transfer chicken to a plate and turn Instant Pot back to Sauté. Add lemon juice, dill weed, garlic powder, carrots, and orzo. Bring to a boil and continue to cook, stirring occasionally, until orzo is tender, about 10 to 12 minutes (check the package for exact cooking time).
Meanwhile, shred chicken with two forks and return to pot when shredded.
When orzo has finished cooking, turn Instant Pot to warm and add spinach and stir to wilt. Taste and adjust seasoning for salt and pepper. You may also add more chicken broth or water if it's thicker than you like.
Stovetop
Dice chicken into bite-sized pieces. In a large stockpot or Dutch oven, heat oil over medium heat. Add diced chicken, celery, onion, salt and pepper. Sauté until onions are translucent, 5 to 6 minutes.
Add broth, water, lemon juice, dill, and garlic; bring to a boil.
Add carrots and orzo and cook for 8 to 10 minutes (follow orzo package directions), until orzo is al dente. Stir in spinach until wilted, and serve!
Notes
If you're not quite ready to serve the soup, wait to add the spinach. Keep the soup warm and add the spinach right before serving so it retains its fresh flavor and color.
To speed up cooking time when making the stovetop version, I recommend dicing the chicken into bite-sized pieces before adding it to the soup. You could cook it whole and shred it if that's what you prefer, but it will slightly increase the cooking time. You can also substitute cooked or rotisserie chicken if you want to make this a super quick and easy recipe.
Leftover soup can be refrigerated for three or four days or frozen for at least 3 months.