There is plenty of information about the on arrival test for VTL available but information on what clinics do what tests for outbound pre departure tests is much more scattered (and different countries have different requirements). https://www.moh.gov.sg/licensing-and...swab-providers has fairly long lists of clinics offering ART or PCR tests but is not sortable by locations and doesn't make clear which clinics will give the necessary documents for a pre departure test as many clinics seem to just support pre event testing.

EDIT: https://www.cdc.gov/coronavirus/2019-ncov/travelers/testing-international-air-travelers.html has the US requirements. Unclear to me from the OP's description if their stopover is long enough to require a test in Singapore.