Do the books referred to in the OT exist? For example, I read about the
“Book of the Annals of the Kings of Judah?” (1 Kings 14:19), the “Book of
the Wars of the Lord”, “Book of Jashar”, “Book of the Annals of Solomon”
and so forth…

The answer is that none of these books have survived. As far as I know, we
do not have extant even a fragment from these documents. This should not
be terrifically surprising, as archaeological evidence, specifically of
written documents, is quite rare from the time period involved, which is
1000-500 BC. What we do learn from the books mentioned in the Old
Testament is that the historical authors of the Old Testament definitely
did consult written sources when producing the histories which ended up in
our Bibles. It would appear that they were making efforts to consult
primary sources when recording their histories of the Hebrew people.

John Oakes, PhD