It seems to me like where a period would be too strong and I want the clause after to be considered equally at the same time or possibly as a counterbalanced thing to whatever is to the left of it
If it were to parse it purely linguistically, it seems like not quite a list of things but perhaps a relevant after thought that a comma would be too weak for and a period too strong
This shouldn’t have a comma because it has a compound predicate. The subject of the sentence is “a semicolon”, and it participates in two predicates: “it clarifies” and “is a complete sentence”.
Your sentence is also logically incorrect because a semicolon neither clarifies nor is a complete sentence.
The proper explanation is: a semicolon separates two closely related independent clauses.