Due to various sales ex-EU in the past, I have some experience dealing the American Airlines reservation systems for flights from the European Union. American Airlines uses Amadeus for certain countries in the EU (in this case Ireland) instead of their usual SABRE.
I would often book directly through American because either I could only find the best fare on American vs. OTAs, or I wanted to use the hold feature. Google Flights would direct me to the americanairlines.eu.amadeus.com link. And when I tried to search for the same flight on aa.com, I was quoted a slightly higher price due to currency conversion to USD. But when I put a reservation on hold through the americanairlines.eu.amadeus.com website, and later tried to find it on the AA.com site to pay for it, I would get this message “Please call to book your trip”