WordPress rewrites standard wordpress urls from /category/post-name/ or whatever your selected permalink type is, into index.php?….
You are adding query vars to a link that is already getting rewritten into index.php?… and thus you are getting a 404.
My advice to you would be to use something similar to an already asked question at Custom page template query_vars or register the query vars properly in WordPress.
WordPress developer reference for adding a query argument -> https://developer.wordpress.org/reference/functions/add_query_arg/
I believe that this should answer your question about how you can handle this.