@JimWarOn the website of the C.S. Forester Society (anybody wants the link, write to me) the Keffer stories are reviewed as fanfiction, first self published and now picked up by a small publisher.
If you want to read stories similar to the Hornblower saga, you may want to try C. Northcote Parkinson's Richard Delancey stories. There are six of them about a Navy officer from Guernsey and his rocky career, often impeded by politics and lack of "interest" in London. Parkinson is best known for "Parkinson's Law", but he was a trained and published naval historian who wrote non-fiction treatises about British naval trade in the early 19th century. He is closer to Aubrey than to Forester in style and accuracy. His books are available at online bookstores or as dead-tree books in the female-warrior-online-store.
PS: He also wrote a fictional biography fo Horatio Hornblower which is fun to read as it fills several gaps in H.H.'s vita that Forester did not close. That work was published with the blessing of the Forester estate.
Of course, Jack Aubrey has redifined the genre with his books, so he is also a tempting alternative to fanfiction, but he is so well known that I won't bore you with my interpretation of his works.
As to my own allusions to H.H., the character is now referred to as "Captain Horace Bugler" in the 2020 re-edit of "In The Navy". He still appears as H.H. in "Ellen", but only for as long as I'll need to fix that. What can I say, I was young and needed the name recognition ๐