> How do you share the "fetching posts" bit of SQL between those three different (parameterized) queries?)

your application has a fetch posts method, that method takes input including (optional) author(s), tag(s), etc., it builds a query that includes WHERE clauses for every provided parameter

the code that converts an author to a WHERE clause can be a function, the point is it outputs a string, or something that is input to a builder and results in a string

i'm not sure what a "fetching posts bit of SQL" is, a query selects specific rows, qualified by where clauses that filter the result set, joins that modify it, etc.