Where did you find the usage of passing in a cookie_jar parameter documented in WWW::Mechanize::Firefox? Reading the code actually helps. You're creating a cookie jar out of thin air and passing that to WWW::Mechanize.

Hint: You're not supposed to create your own HTTP::Cookies::MozRepl, because they always live within the Firefox instance. You can retrieve the cookies from Firefox using $firefox->cookies().

I'm not sure if it's possible to directly pass in all cookies to WWW::Mechanize. For sanitary and sanity reasons, I would only pass on the relevant cookies of the site you're automating, not all cookies.