Am I understanding the rules right here:

USA->AMS, <24 hour transit -> separate ticket to Italy would not require a PCR test for AMS because the “connection” is under 24 hours as long as I have proof of an onward ticket, even though I’m clearing immigration in AMS?

and then flying Italy -> back to AMS as a non EU citizen who has been in the USA in the past 14 days, I would need a PCR in addition to proof of vaccination to enter AMS as I do not satisfy the >14 day “clean” policy yes?

thanks so much.