Codex extension crashes the page

### Is there an existing issue for this?

- [x] I have searched the existing issues

### OS/Web Information

- Web Browser: Chrome
- Local OS: Windows 11
- Remote OS: Debian Trixie
- Remote Architecture: x64
- `code-server --version`: 4.116.0

### Steps to Reproduce

Spend a day closing issues with codex.

### Expected

No issue

### Actual

Relyably within 4-5 hours you will start getting

I am currently poisiting that something is being stored into indexdb or something client side (ideas?) thats causing a crash.

Seems to be getting worse too.

### Logs

```shell
Nothing of interest on the server side.
```

### Screenshot/Video

_No response_

### Does this bug reproduce in native VS Code?

No, this works as expected in native VS Code

### Does this bug reproduce in VS Code web?

I did not test VS Code web

### Does this bug reproduce in GitHub Codespaces?

I did not test GitHub Codespaces

### Are you accessing code-server over a secure context?

- [x] I am using a secure context.

### Notes

I have tested removing nearly every other extension, it appears to be code-server + codex.

Happy to get logs if you can provide some indication on how to, there doesnt appear to be anything on the server side as this seems to trigger a client side bug.