fix(agents): skip auth profile cooldown for timeout failures

A timeout is model/network-specific, not an auth issue. Marking the
auth profile as failed on timeout poisons fallback models on the same
provider (e.g. gpt-5.3 timeout would block gpt-5.2 via shared profile
cooldown). The prompt-phase path already guards against this; this
aligns the post-response timeout path to match.

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

src/agents/pi-embedded-runner/run.ts

@@ -960,13 +960,18 @@ export async function runEmbeddedPiAgent(
                 timedOut || assistantFailoverReason === "timeout"
                   ? "timeout"
                   : (assistantFailoverReason ?? "unknown");
-              await markAuthProfileFailure({
-                store: authStore,
-                profileId: lastProfileId,
-                reason,
-                cfg: params.config,
-                agentDir: params.agentDir,
-              });
+              // Skip cooldown for timeouts: a timeout is model/network-specific,
+              // not an auth issue. Marking the profile would poison fallback models
+              // on the same provider (e.g. gpt-5.3 timeout blocks gpt-5.2).
+              if (reason !== "timeout") {
+                await markAuthProfileFailure({
+                  store: authStore,
+                  profileId: lastProfileId,
+                  reason,
+                  cfg: params.config,
+                  agentDir: params.agentDir,
+                });
+              }
               if (timedOut && !isProbeSession) {
                 log.warn(
                   `Profile ${lastProfileId} timed out (possible rate limit). Trying next account...`,