refactor(auth): rename loginType to loginStatus and update related logic

src/stores/auth/auth-context.tsx

@@ -33,7 +33,7 @@ interface AuthState {
   isLoading: boolean;
   errorMessage: string | null;
   isSuccess: boolean;
-  loginType: MachineContext["loginType"];
+  loginStatus: MachineContext["loginStatus"];
 }
 
 const AuthStateCtx = createContext<AuthState | null>(null);
@@ -62,7 +62,7 @@ export function AuthProvider({ children }: AuthProviderProps) {
         state.matches("loadingOAuth"),
       errorMessage: state.context.errorMessage,
       isSuccess: state.matches("success"),
-      loginType: state.context.loginType,
+      loginStatus: state.context.loginStatus,
     }),
     [state],
   );