My experience has been all TATL but might be helpful. In person document verification has been required at check in since early April on all international flights. A duty manager override has been required since then for all non-nationals (although this appears to have been relaxed lately). Physical documentation has been required which matches exactly the guidelines outlined on the IATA website (COVID travel map) for the destination and each stop along the way. In the past, check in has for the most part just taken our word that we have it, now they are required to review it. For example I am a dual Cdn/Danish citizen, I was refused boarding in April because I didn't have my Danish passport with me even though AC requires I travel on my Cdn passport. Although the requirements for entrance have been mostly static for some time, initially they were changing in some cases daily. The driver is of course financial and the avoidance of penalties for carrying undocumented passengers.

I have found it extremely helpful to contact the concierge at the arrival or transit stop to advise of any requirements. They seem to be able to over-ride.