I've never been able to understand why mail apps insist on the word Compose. Is it an American thing? I've never wanted to compose a piece of text, and never heard the word used in that way.

It's from the older phrase "compose a letter". Since letters were replaced with email, the phrase became "compose an email".

It's the word gmail uses as well.

no the word gmail uses is "+"

I do see a "+" front and center though,which is not the case on apple devices. even if I don't know what compose means, I do know that + probably means creating a email

To be clear: whatever the button is called, it doesn't have any text on iOS (which, as far as I can tell, is what OP was talking about). It's just an icon of a pencil writing on paper.

To be even clearer: It's literally one of only 4 buttons on the main Mail screen (the others being Back, Edit, and Filter). If you just go to Mail and don't even attempt a guess, that's on you.

What word would you use to describe the action of creating a new message?

write or create or new

Sounds a bit grandiose from here in California.

Compose is defined as putting together many pieces into one coherent work. Most people associate it with music, where composers put together notes until they make up a piece of music. In the mail app context it also makes perfect sense as you are composing a larger piece of work (your letter) from smaller individual elements (words).

TL;DR - Compose is the correct word to use.