Heat oil and melt butter in the Instant Pot using the SAUTE setting. Add the onions and celery, and cook for 2 minutes or until the onion is soft and translucent. Add garlic and cook for a minute. Switch off the saute setting.
Add chicken or vegetable stock, raw chicken breasts, carrot, fresh thyme, salt, and pepper.
Secure the lid and set the vent to SEALING. Select the PRESSURE COOK/MANUAL setting and set the cooking time for 7 minutes at high pressure. The Instant Pot will take around 7-8 minutes to come to pressure and start cooking. When the cooking program ends, quickly release the steam.
Carefully remove the lid, and take the chicken out and dice or shred it into pieces then set aside.
On the Instant Pot choose the SAUTE-low setting, and add in the gnocchi and let the soup simmer until the gnocchi float to the top (the recommended cooking time is usually written on the package). Switch off the saute setting.
Stir in the half and half, spinach, and chicken. Give the spinach a few minutes to wilt, and the soup is ready to be served!