refactor(frontend): create centralised auth manager (#24)

- Resolves #17

Reviewed-on: #24

frontend/src/auth/AuthContext.ts

@@ -0,0 +1,20 @@
+import { createContext } from "react";
+import type { User } from "../utils/types.ts";
+
+type AuthContextValue = {
+    /** The currently authenticated user, or null when logged out. */
+    user: User | null;
+    /** True until the initial "who am I" request has resolved. */
+    loading: boolean;
+    /** Exchange a Google credential for a session, then load the user. */
+    login: (googleCredential: string) => Promise<void>;
+    /** End the session and clear the user. */
+    logout: () => Promise<void>;
+    /** Re-fetch the current user (e.g. after a profile change). */
+    refresh: () => Promise<void>;
+};
+
+const AuthContext = createContext<AuthContextValue | null>(null);
+
+export { AuthContext };
+export type { AuthContextValue };