oh weird you don’t have a settings editor button. Probably need to upgrade your Discourse.
did you refresh the page after changing the settings?
FWIW, here are my settings on my dev local Discourse install. I edited the default settings for the first one that goes to Meta, and also added one to my FAQ page just to make sure non-default ones work.
Meta, will open in a new tab to Discourse Meta, https://meta.discourse.org, vdo, blank, remove
Most Liked, Posts with the most amount of likes, /latest/?order=op_likes, vdo, self, keep
Privacy, Our Privacy Policy, /privacy, vdm, self, keep
FAQ, Frequently Asked Questions, /faq, vdm, self, keep
Here is the result with a test user (non admin).
As a word of advice, I would limit the number of links to one or two for mobile view. That header gets crowded awfully fast in mobile/ small screen views, especially for anonymous users with the login/sign up buttons.