A commenter points to this Google nGram graph so we can see the history of the phrase used by by the Democratic National Convention for one of their 14 identity politics communities: "European and Mediterranean Americans" (of whom, we are informed by the Democrats: "The culture and history of European and Mediterranean Americans contribute to America’s unique fabric.")
In other words, from 1800 through 2008 (the latest year Google allows), the phrase "European and Mediterranean Americans" appeared in zero books known to Google.
It appears that the term was chosen by the Democrats to represent what used to be called the "white ethnic" vote, but without using the word "white."
The phrase "Mediterranean American" was probably chosen to represent Christian Lebanese, who aren't from Europe in a geographic sense, but are a prosperous group. The leaves up in the air "Armenians," who used to have a Black Sea coast and have a fairly Mediterranean culture.