Does this screening service program already exist at airports? If so, which ones?

Yes, there is one operating RSSP location at LAX and locations at MSP, ATL, LGA, and LAX which are approved but are not operating at this time.

The LAX RSSP location began operating in January 2020 with the operator Private Suite (PS).

MSP - is on hold at this time due to COVID-19 and low passenger volume.
LGA - is in the screening equipment procurement stage with LaGuardia Gateway Partners.
ATL - is in the agreement signature phase with the City of Atlanta, Signature Flight Services, and PS.
LAX - a second RSSP location at LAX to be operated by Delta Air Lines was recently approved in June 2022.