fix(#411): classifyAuthError — return null for normal 401/session-expired instead of 'backend'

Normal authentication failures (401 Unauthorized, 403 Forbidden, session
expired) are not backend errors — they simply mean the user isn't logged in.
Previously these fell through to the `instanceof Error` catch-all and returned
"backend", causing a misleading "having trouble connecting" banner.

Now classifyAuthError explicitly checks for invalid_credentials and
session_expired codes from parseAuthError and returns null, so the UI shows
the logged-out state cleanly without an error banner.

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

apps/web/src/lib/auth/auth-context.tsx

@@ -41,6 +41,9 @@ const AuthContext = createContext<AuthContextValue | undefined>(undefined);
  * Classify an error into an {@link AuthErrorType} using the centralised
  * {@link parseAuthError} utility.
  *
+ * Normal authentication failures (401 Unauthorized, session expired) return
+ * `null` so the UI simply shows the logged-out state without a banner.
+ *
  * Defaults unrecognised `Error` instances to `"backend"` rather than `null`
  * so that unexpected failures surface a "having trouble connecting" banner
  * instead of silently logging the user out.
@@ -49,7 +52,10 @@ function classifyAuthError(error: unknown): AuthErrorType {
   const parsed = parseAuthError(error);
   if (parsed.code === "network_error") return "network";
   if (parsed.code === "server_error") return "backend";
-  // For unrecognised errors, default to "backend" rather than null
+  // Normal auth failures (not logged in, session expired) are not errors —
+  // return null so the UI shows logged-out state without a banner
+  if (parsed.code === "invalid_credentials" || parsed.code === "session_expired") return null;
+  // For truly unrecognised errors, default to "backend" rather than null
   // (safer to show "having trouble connecting" than silently log out)
   if (error instanceof Error) return "backend";
   return null;