Leaving EU, with layover in another EU country. Do we need an EU pet passport?

Hello all. We will be flying from Ireland -> Amsterdam -> US with KLM. We are bringing our two cats with us.

Our dog will follow later in cargo with Lufthansa (Ireland -> Frankfurt -> US).

I can't seem to find a concrete answer to this... but I am wondering if we need an EU pet passport, or if a health cert will be sufficient? We are travelling in less than 1 week and I'm not sure we would get an EU pet passport that fast.

My understanding of EU pet passport would be if your destination is within the EU, and you're clearing customs in the EU. But if we're not clearing customs (ie: it's a layover), and we won't be leaving the airport in Amsterdam/Frankfurt with our pets, an EU pet passport would not be required, and an animal health cert would be sufficient.

Could someone who has done similar advise?