feat: clear local authentication token when switching from local auth mode

frontend/src/components/providers/AuthProvider.tsx

@@ -1,14 +1,26 @@
 "use client";
 
 import { ClerkProvider } from "@clerk/nextjs";
-import type { ReactNode } from "react";
+import { useEffect, type ReactNode } from "react";
 
 import { isLikelyValidClerkPublishableKey } from "@/auth/clerkKey";
-import { getLocalAuthToken, isLocalAuthMode } from "@/auth/localAuth";
+import {
+  clearLocalAuthToken,
+  getLocalAuthToken,
+  isLocalAuthMode,
+} from "@/auth/localAuth";
 import { LocalAuthLogin } from "@/components/organisms/LocalAuthLogin";
 
 export function AuthProvider({ children }: { children: ReactNode }) {
-  if (isLocalAuthMode()) {
+  const localMode = isLocalAuthMode();
+
+  useEffect(() => {
+    if (!localMode) {
+      clearLocalAuthToken();
+    }
+  }, [localMode]);
+
+  if (localMode) {
     if (!getLocalAuthToken()) {
       return <LocalAuthLogin />;
     }