This doesn't address auth(orization), i.e. "permissions", and it also introduces worse usability for non-native speakers. "Sign in" and "sign up" are hard to distinguish for some demographics (especially non-native speakers) so putting them side by side like that while creating nice symmetry makes it harder to understand.

I think some research by Nielsen twenty-ish years ago suggested using "Sign in"/"Sign out" and "Register". It feels like "Log in"/"Log out" won out on most of the web (e.g. Facebook uses "Log in"/"Log out" and "Sign up").