I didn't mind being pretty strict regarding the URL validation; I don't even care too much about the fact of allowing "https:testhello", but I don't like that Chrome, Safari, and maybe others are opening <a href="https:testhello"> link </a> as "https://keepthis.site/https:testhello" but Firefox opens it as a new URL without "https://keepthis.site" which is the behavior I would expect.
I am going to re-implement the validation with simpler rules. Many thanks for your feedback.