feat: add sign-out redirect URL and enhance sign-in redirect handling

frontend/src/components/providers/AuthProvider.tsx

@@ -7,12 +7,19 @@ import { isLikelyValidClerkPublishableKey } from "@/auth/clerkKey";
 
 export function AuthProvider({ children }: { children: ReactNode }) {
   const publishableKey = process.env.NEXT_PUBLIC_CLERK_PUBLISHABLE_KEY;
+  const afterSignOutUrl =
+    process.env.NEXT_PUBLIC_CLERK_AFTER_SIGN_OUT_URL ?? "/";
 
   if (!isLikelyValidClerkPublishableKey(publishableKey)) {
     return <>{children}</>;
   }
 
   return (
-    <ClerkProvider publishableKey={publishableKey}>{children}</ClerkProvider>
+    <ClerkProvider
+      publishableKey={publishableKey}
+      afterSignOutUrl={afterSignOutUrl}
+    >
+      {children}
+    </ClerkProvider>
   );
 }