I’m not sure I ever answered this question.
I say both. It depends on the context.
When I was growing up in1960s California, I learned both at home and at school to use the long A sound when speaking in English and the “ah” sound when using Latin. That’s how the sisters at my school spoke. And that is how the American born priests in my parish spoke. (I can’t really remember how the foreign born priests pronounced it when speaking in English but probably more of an “eh” sound.)
I grew up associating the “ah” pronunciation with people who lived on the East Coast of the United States, people who spoke with upper class English accents, and liturgical protestants.
There were a lot of discussions on the “proper” pronunciation of “Amen” here at Catholic Answers over the years, many with people shouting that it is a Catholic versus Protestant thing. I had actually saved some links but those links don’t work now. I’m guessing the conversations were not all carried over during the forum switchover. For Catholics, the differences in pronunciation seem to be VERY regional.
As far as "ay’ being a protestant innovation, that is true in as much as Protestants probably normalized English translations of Latin prayers. But as to the pronunciation of words in English (including “amen”) google “the great vowel shift” for info on how “ah” turned into “eh” and/or “ay”.