Keep in mind, Ryanair sets no rules for what you need for documentation. The website is stating reality, have whatever documents you need or you may not board. Individual countries set requirements, and requirements on both ends may come into play.
So if you are flying to a country that requires a test...guess what...you need a test...Ryanair did not set the rule...the country did, Ryanair, as an international carrier is just responsible for checking, same with the form of vaccination proof.
For traveling within Italy by plane, Italy has required proof of vaccination or test, basically their requirements for a Green Pass. Italy does not issue green passes, so they accept the CDC card for flights (Fully vaccinated, plus a booster under certain conditions), they likely require the same for international flights. Then you need to know what Spain requires, which right now appears to be proof of vaccination, which your CDC card will suffice, depending on booster status and timing.
I flew several Ryanair flights (within Italy) in September, my CDC card and passport was checked three times one flight (to get into the airport, at check-in, and at boarding) and similar the other boarding, all no problem with the CDC card.