fix(auth): prevent login page freeze on OAuth sign-in failure

The login page froze after clicking "Continue with Authentik" because
signIn.oauth2() resolves (not rejects) on server 500, leaving the
button stuck in "Connecting..." state permanently.

- Handle the .then() case to detect error/missing redirect URL and
  reset loading state with a user-facing error message
- Log BetterAuth silent 500 responses that bypass NestJS error handling
- Enable BetterAuth error-level logger for diagnostic visibility

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/web/src/app/(auth)/login/page.tsx

@@ -128,12 +128,31 @@ function LoginPageContent(): ReactElement {
     setError(null);
     const callbackURL =
       typeof window !== "undefined" ? new URL("/", window.location.origin).toString() : "/";
-    signIn.oauth2({ providerId, callbackURL }).catch((err: unknown) => {
-      const message = err instanceof Error ? err.message : String(err);
-      console.error(`[Auth] OAuth sign-in initiation failed for ${providerId}:`, message);
-      setError("Unable to connect to the sign-in provider. Please try again in a moment.");
-      setOauthLoading(null);
-    });
+    signIn
+      .oauth2({ providerId, callbackURL })
+      .then((result) => {
+        // BetterAuth returns Data | Error union — check for error or missing redirect URL
+        const hasError = "error" in result && result.error;
+        const hasUrl = "data" in result && result.data?.url;
+        if (hasError || !hasUrl) {
+          const errObj = hasError ? result.error : null;
+          const message =
+            errObj && typeof errObj === "object" && "message" in errObj
+              ? String(errObj.message)
+              : "no redirect URL";
+          console.error(`[Auth] OAuth sign-in failed for ${providerId}:`, message);
+          setError("Unable to connect to the sign-in provider. Please try again in a moment.");
+          setOauthLoading(null);
+        }
+        // If data.url exists, BetterAuth's client will redirect the browser automatically.
+        // No need to reset loading — the page is navigating away.
+      })
+      .catch((err: unknown) => {
+        const message = err instanceof Error ? err.message : String(err);
+        console.error(`[Auth] OAuth sign-in initiation failed for ${providerId}:`, message);
+        setError("Unable to connect to the sign-in provider. Please try again in a moment.");
+        setOauthLoading(null);
+      });
   }, []);
 
   const handleCredentialsLogin = useCallback(