So you don’t have to have a type certificate in the a/c your flying if it’s a commercial airliner? I’d be really surprised it that were the case. The FAA has to have flight standards for crews operating a/c coming into this country.
If the aircraft weighs more the 12,500 pounds or is powered by turbojet engines, you need a type rating added to your commercial certificate or your airline transport certificate.
But foreign countries have their own certification agencies. The European Union has one agency called EASA that has a common certification process for all the participating members. Canada has their own certification process through Transport Canada. Mexico, the South American countries, etc. all have their own certification agencies, like our FAA. So a FAA database is not systematically tracking foreign pilots.