Terminal tab actions become unresponsive during frequent OSC title updates

Does this issue occur when all extensions are disabled?: Yes

- VS Code Version: 1.129.1
- OS Version: macOS 26.5.2 (25F84), arm64

Steps to Reproduce:

1. Open two or more integrated terminals so the terminal tabs list is visible.
2. In one of them, run:

```bash
i=0; while :; do i=$((i + 1)); printf '\033]0;working-%06d\007' "$i"; sleep 0.05; done
```

3. While it is running, use the trash, split, or rename action in the terminal tabs list.

Actual behavior:

- Trash and split do nothing.
- Rename opens briefly and immediately closes.
- Context-menu **Kill Terminal** and the Command Palette kill command still work.
- The actions work again after stopping the loop with `Ctrl+C`.

Expected behavior:

Terminal tab actions remain usable during title updates.

Additional information:

This was first noticed with Codex CLI 0.144.6: it occurs while Codex is working and stops when Codex becomes idle. These settings do not prevent it:

```json
"terminal.integrated.tabs.allowAgentCliTitle": false,
"terminal.integrated.shellIntegration.enabled": false
```

Related: [#279443: Rename Terminal Immediately Exits](https://github.com/microsoft/vscode/issues/279443) — closed as not planned, but the reproduction above may explain its root cause.