I am confused. What do you mean by “browser URL”? Do you mean the URL of the page that the user accessed? How is that not essential? How is it specific to the user’s device?
[1] https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CEL...
Your citation does not mention URLs or clarify why they might be non-essential.
If you're using it to display a page (say: React Router), then it's essential functionality.
If you're using the URL to propagate a unique hash between pages that is used to identify the user for marketing purposes, then it requires consent.