Add React frontend and Sinbad2IA LLM integration.

Introduce a full Vite/React UI for exams, auth, materials, images, generation, and export.
Adapt backend for Sinbad2IA chat API, bcrypt passwords, CORS on port 5173, and schema migrations.

frontend/src/context/AuthContext.jsx

@@ -0,0 +1,106 @@
+import {
+  createContext,
+  useCallback,
+  useContext,
+  useEffect,
+  useState,
+} from "react";
+import {
+  clearToken,
+  getToken,
+  onUnauthorized,
+  setToken,
+} from "../api/client";
+import * as authApi from "../api/auth";
+
+const AuthContext = createContext(null);
+
+export function AuthProvider({ children }) {
+  const [user, setUser] = useState(null);
+  const [loading, setLoading] = useState(true);
+
+  const logout = useCallback(() => {
+    clearToken();
+    setUser(null);
+  }, []);
+
+  // Carga inicial: si hay token, intenta recuperar el usuario.
+  useEffect(() => {
+    let active = true;
+    async function bootstrap() {
+      if (!getToken()) {
+        setLoading(false);
+        return;
+      }
+      try {
+        const me = await authApi.getMe();
+        if (active) setUser(me);
+      } catch {
+        clearToken();
+      } finally {
+        if (active) setLoading(false);
+      }
+    }
+    bootstrap();
+    return () => {
+      active = false;
+    };
+  }, []);
+
+  // Reacciona a 401 global (token caducado).
+  useEffect(() => onUnauthorized(() => logout()), [logout]);
+
+  const finishLogin = useCallback(async (tokenResponse) => {
+    setToken(tokenResponse.access_token);
+    const me = await authApi.getMe();
+    setUser(me);
+    return me;
+  }, []);
+
+  const login = useCallback(
+    async (credentials) => {
+      const res = await authApi.login(credentials);
+      return finishLogin(res);
+    },
+    [finishLogin]
+  );
+
+  const loginWithGoogle = useCallback(
+    async (idToken) => {
+      const res = await authApi.loginWithGoogle(idToken);
+      return finishLogin(res);
+    },
+    [finishLogin]
+  );
+
+  const register = useCallback(async (payload) => {
+    await authApi.register(payload);
+    // Tras registrar, iniciamos sesión automáticamente.
+    const res = await authApi.login({
+      email: payload.email,
+      password: payload.password,
+    });
+    setToken(res.access_token);
+    const me = await authApi.getMe();
+    setUser(me);
+    return me;
+  }, []);
+
+  const value = {
+    user,
+    loading,
+    isAuthenticated: !!user,
+    login,
+    loginWithGoogle,
+    register,
+    logout,
+  };
+
+  return <AuthContext.Provider value={value}>{children}</AuthContext.Provider>;
+}
+
+export function useAuth() {
+  const ctx = useContext(AuthContext);
+  if (!ctx) throw new Error("useAuth debe usarse dentro de AuthProvider");
+  return ctx;
+}