"This reminds me of books like
Bram Stoker's "Dracula"
Mary Shelley's "Frankenstein"
Where the whole story is told by long detailed letters between characters."
This is called an "epistolary novel."
Pamela; or, Virtue Rewarded," by Samuel Richardson, published in 1740, is often considered to be "the first English novel." It is an epistolary novel.
I haven't really paid much attention, but certainly the form still exists. Up the Down Staircase, by Bel Kauffman, a bestseller in 1964, is wonderful--very funny and quite touching. It is the story of a high-school teacher, told in the form of a series of informal written notes between two teachers at the school. It's written in colloquial, informal English, in short sentences, but it is definitely an epistolary novel.