Air Premia doesn't participate in TSA PreCheck.
https://www.tsa.gov/precheck/participating-airlines

Global Entry is tied to your passport, so there's no need to enter your KTN. The KTN is only needed for TSA reasons.

Edit: To be explicit, you'll still get GE privileges when entering the USA. The airline will capture your US passport number, either at check-in, or when you entered it when purchasing the ticket. That info will be transmitted to the USCBP via the airline eAPIS data dump pre-departure, as required by all airlines entering the USA. The USCBP will know you're coming, and the GE kiosks will be ready for you.