AniListSearch hardcoded false for the authenticated flag to
AniListQuery, forcing anonymous searches even with a valid AniList
session. Pass a.CheckIfAniListLoggedIn() instead so the stored token
is attached when available, enabling user-specific data and
authenticated rate limits while keeping anonymous search as fallback.
In CheckIfMyAnimeListLoggedIn and MyAnimeListLogin the keyring lookups
assigned MyAnimeListAccessToken to refreshToken and
MyAnimeListRefreshToken to accessToken. Downstream code checks
len(accessToken.Data) for login state and assigns
accessToken.Data -> myAnimeListJwt.AccessToken, so the swap gated
login on the refresh token and stored each token in the wrong field.
Swap the variable names to match their keyring keys so login detection,
JWT restoration, and the empty-token fallback in MyAnimeListLogin use
the correct values.