Address second review pass: fix start-time race + minor cleanups

- M1 (race): don't mount the host AWS dir for static-credential Bedrock.
  sync_bedrock_credentials() is the sole writer of ~/.aws/credentials in
  that mode, and mounting /tmp/.host-aws let the entrypoint's
  `rm -rf ~/.aws; cp -a` race that write at startup (only when a global
  aws_config_path was also set). Static keys + AWS_REGION env are
  self-sufficient and don't need the host config, so skipping the mount
  removes the dual-writer entirely.
- L-a: exit codes are now read via wait_for_exec_exit(), which polls
  inspect_exec until the exec reports finished, so a non-zero tar/cred
  exit isn't missed by reading exit_code too early. The backup only fails
  on a definitively non-zero code (falls back to the empty-output check
  if undeterminable).
- L-b: fixed two comments that referenced the old
  write_bedrock_static_credentials name (now sync_bedrock_credentials).
- L-c: entrypoint only rewrites ~/.claude.json when awsAuthRefresh is
  actually present, avoiding a needless jq reformat on every non-SSO
  start.
- L-d: backup script traps EXIT to remove its mktemp staging dir even
  when tar fails, so failed backups don't accumulate temp dirs (with the
  sanitized config copy) in the container.

L-e (drop routing) is a non-issue: the layout is tabbed, so only one
terminal pane is ever visible; the active-guard routing is correct.

Verified the race fix, trap cleanup, grep guard, and exit-code polling.
cargo check / tsc / vitest all pass.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

app/src-tauri/src/docker/exec.rs

@@ -344,14 +344,30 @@ pub async fn exec_oneshot_env_status(
         StartExecResults::Detached => return Err("Exec started in detached mode".to_string()),
     }
 
-    // Exit code is only available after the process has finished (the stream above
-    // has drained), so inspect now.
-    let exit_code = docker
-        .inspect_exec(&exec.id)
-        .await
-        .map_err(|e| format!("Failed to inspect exec: {}", e))?
-        .exit_code
-        .unwrap_or(0);
+    // The output stream draining doesn't strictly guarantee inspect_exec has the
+    // final exit_code populated yet, so poll until the exec reports finished.
+    let exit_code = wait_for_exec_exit(&exec.id).await.unwrap_or(0);
 
     Ok((combined, exit_code))
 }
+
+/// Poll `inspect_exec` until the exec reports finished and return its exit code.
+/// Returns `None` if the code can't be determined (inspect error, or the exec
+/// doesn't report finished within ~1s — which shouldn't happen once its output
+/// stream has drained).
+pub async fn wait_for_exec_exit(exec_id: &str) -> Option<i64> {
+    let docker = get_docker().ok()?;
+    for _ in 0..40 {
+        match docker.inspect_exec(exec_id).await {
+            Ok(info) => {
+                if info.running != Some(true) {
+                    // Finished: use the reported code (default 0 if somehow absent).
+                    return Some(info.exit_code.unwrap_or(0));
+                }
+            }
+            Err(_) => return None,
+        }
+        tokio::time::sleep(std::time::Duration::from_millis(25)).await;
+    }
+    None
+}