James, I can speak to the Amsterdam connection as we've flown in and out of the airport a few times since the COVID situation began. Yes, American citizens traveling on a US Passport can connect at AMS, but you will have stay AIRSIDE. Currently, US citizens cannot enter the Netherlands. To meet the criteria to enter the Netherlands (as outlined in the Schiphol statement above), you'd have to be traveling on an EU passport, be from one of the "EU-approved" countries (the USA is not), have an EU Visa, or be an "essential traveler" with pre-arranged clearance. Of course, these restrictions/rules could all change tomorrow. (For example, we're flying to Copenhagen this weekend but had to get an "exception" to the 6-day-stay minimum in Denmark).
Schiphol is relatively quiet these days, with minimal stores open and very decreased traffic. In June, my wife flew back-and-forth to the USA using her Dutch Visa to reenter The Netherlands on her return. No other Americans were in line at passport control or at the baggage carousel. There were US citizens on her return flight from ATL, but they were all connecting, many heading to the Far East (or other "approved" destinations).
Disappointedly, COVID checks at AMS have been quite inconsistent - frankly, pretty lax in our travels through the airport. That may change as recently we've seen an increase in the number of in-country COVID cases. Unfortunately, the Netherlands has recently "hit the quarantine list" for a few countries - like the UK - so it seems the rules of entry/exit seem to change daily. (There goes our October weekender to London...)