A friend of mine just arrived with their small dog out of the US. I asked them what airline they took and will forward the answer when i get it.
Once in Thailand. NOK is the only airline that allows transporting small animals in the cabin. You have to contact them directly because you cant purchase that ticket online.
As long as you are laying over at the same airport you are landing in . If you have to transfering airports (Narita & Haneda) you need to have your Covid test.