Rememberance: Selected Correspondence of Ray Bradbury (November 2023), begins with letters from the year of Lovecraft’s death 1937 and ends in 1957. The letters are presented in themed and clustered sections, and mostly face towards his contemporaries during that period. The book is substantial, but is said to be merely a taster for around 14,000 letters so far traced by the Center for Ray Bradbury Studies.
The hardback is available (though Amazon UK can’t ship it to me, so there may be region restrictions), but the paperback has yet to appear. Amazon UK says it’s due in November 2024.
The book does not mention Lovecraft but there are many references to Weird Tales. My review of it in the Wall Street Journal is here:
https://www.wsj.com/arts-culture/books/remembrance-review-a-busy-life-at-the-typewriter-464007b0