If you want pastina that has more broth and isn't as thick and porridge-like, then cook the pasta separately in a pot of boiling water. Serve the pasta separately and everyone can add their own cooked pasta to their bowl of broth and chicken.
If you prefer white meat you can use chicken breasts instead of thighs. Chicken breasts vary in size so it might take a little longer than 15 minutes to reach an internal temperature of 165F. Just like thighs, let the meat rest for 10 minutes or more before shredding the meat.
For a short-cut, use rotisserie chicken. You can add the cooked chicken to the pot after the pasta cooks.
Leftovers will stay fresh for up to 4 days in the refrigerator. The consistency will get really thick as the pasta continues to absorb the broth.