refactor(auth): separate auth and author responsibilities and centralize auth client creation

- Replace manual axios auth client with createApiClient in auth context
- Decouple domain author logic from auth provider
- Make AuthorModel extend AuthUser explicitly
- Route login/register/logout exclusively through auth package
- Derive application-level currentUser from auth identity
- Fix provider hierarchy and hook usage across Blog and Profile
- Align main.jsx to use base AuthProvider + AuthorProvider layering

auth/src/contexts.tsx

@@ -0,0 +1,96 @@
+import React, { createContext, useContext, useEffect, useState } from "react";
+import { tokenStore } from "./token";
+import { createApiClient } from "./axios";
+import { AuthUser } from "./models";
+
+interface AuthContextModel {
+  currentUser: AuthUser | null;
+  token: string | null;
+  loading: boolean;
+  error: string | null;
+  login(username: string, password: string): Promise<void>;
+  register(username: string, password: string): Promise<void>;
+  logout(): void;
+}
+
+const AuthContext = createContext<AuthContextModel | undefined>(undefined);
+
+export function AuthProvider({
+  children,
+  authBaseUrl,
+}: {
+  children: React.ReactNode;
+  authBaseUrl: string;
+}) {
+  const [currentUser, setCurrentUser] = useState<AuthUser | null>(null);
+  const [token, setToken] = useState<string | null>(tokenStore.get());
+  const [loading, setLoading] = useState(false);
+  const [error, setError] = useState<string | null>(null);
+
+  const auth = createApiClient(authBaseUrl);
+
+  const login = async (username: string, password: string) => {
+    try {
+      setLoading(true);
+      setError(null);
+
+      const res = await auth.post("/login", { username, password });
+      const { access_token, user } = res.data;
+
+      tokenStore.set(access_token);
+      setToken(access_token);
+      setCurrentUser(user);
+    } catch (e: any) {
+      setError(e.response?.data?.detail ?? "Login failed");
+    } finally {
+      setLoading(false);
+    }
+  };
+
+  const register = async (username: string, password: string) => {
+    try {
+      setLoading(true);
+      setError(null);
+
+      await auth.post("/register", { username, password });
+    } catch (e: any) {
+      setError(e.response?.data?.detail ?? "Registration failed");
+    } finally {
+      setLoading(false);
+    }
+  };
+
+  const logout = () => {
+    tokenStore.clear();
+    setToken(null);
+    setCurrentUser(null);
+  };
+
+  const fetchCurrentUser = async () => {
+    if (!token) return;
+    try {
+      const me = await auth.get("/me");
+      setCurrentUser({ ...me.data });
+    } catch {
+      logout();
+    }
+  };
+
+  useEffect(() => {
+    fetchCurrentUser();
+  }, [token]);
+
+  return (
+    <AuthContext.Provider
+      value={{ currentUser, token, loading, error, login, logout, register }}
+    >
+      {children}
+    </AuthContext.Provider>
+  );
+}
+
+export function useAuth(): AuthContextModel {
+  const ctx = useContext(AuthContext);
+  if (!ctx) throw new Error("useAuth must be used inside AuthProvider");
+  return ctx;
+}