US citizens connecting AMS non-Schengen to non-Schengen (ATL → AMS → CPT) — do we need passport control or EES registration?

Hi! I'm hoping someone can help clarify something about our upcoming connection at Amsterdam Schiphol.

We are two US citizens traveling on a single booking from Little Rock, Arkansas → Atlanta (Delta) → Amsterdam (Delta) → Cape Town (KLM). We arrive in Amsterdam on May 30th at 7:25 AM.

Since we are connecting from one non-Schengen country (USA) to another non-Schengen country (South Africa), will we need to go through passport control or EES registration during our layover? Or do we stay airside in the international transit zone and proceed directly to our KLM gate?

Thank you!