The term "parasocial relationship" is usually reserved for actual people. You could stretch it to include fictional characters, but it misses out on some of the reasons we coined the term.

For example, you can't stalk Harry Potter. There are surely people stalking JK Rowling, and that is a better example of a parasocial relationship.

Not all parasocial relationships are pathological. It's just a useful extreme to illustrated why the distinction exists.