On Instant Pot, press "saute" button. After 1 minute, add olive oil to IP insert. Wait 1 minute, then add onion and garlic. Saute, stirring often, for 1 minute. Add carrots and celery and saute for 2 minutes. Add diced chicken and Italian seasoning and cook, stirring often, until almost done.
Add remaining ingredients, making sure the noodles are just covered with liquid.
Cover the IP with lid and set the pressure valve to "sealing" position. Newer models do it on their own.
Press "manual" and set the timer to 6 minutes. Make sure your Instant Pot is set to high pressure. The pressure cooker will beep and start coming to pressure, which can take about 12 minutes.
When the cooking time is up, press the "cancel/off" button. Let the pressure release naturally for 5 minutes (to let the foam from cooking noodles to fall), then quick release any remaining pressure by switching the valve to venting position.
Carefully open the lid, away from your face. Stir the soup. Let cool and serve. Adjust seasoning as needed.