if your antigen test is positive you could still be shedding - and spreading virus. Antigen tests show presence of spreadable virus.
PCR tests for a part of the virus that may not indicate spreadable virus but present viral particles.
PCR is the one that may be present for 30 days or more, but the patient is not transmitting virus.
Antigen, since it indicates spreadable virus is the most important while travelling - or even going about your business at home.
The one you want for travel is the antigen test, and if you are post-infectious it will be negative.
If its positive you can still be spreading virus even if you are no longer symptomatic.