Copilot Chat does not work

**Edit** by @code-asher:

There have been a few reported issues: either Copilot does not install, installs but does not run, runs but signing in does not work, or runs but not correctly.

Not sure what we can do, it is not something we can debug because running Copilot in code-server is a violation of the license (as far as we understand) and it is closed source.

Maybe we will need to add documentation that Copilot does not work, or maybe there are other similar extensions we can test that will reveal what the underlying issues are, assuming they are code-server issues and not something in the extension.

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### Is there an existing issue for this?

- [x] I have searched the existing issues

### OS/Web Information

- Web Browser: Brave
- Local OS: macOS
- Remote OS: Debian
- Remote Architecture: x86_64
- `code-server --version`: 1.102.3
6f3d0a7e5ae5f6623e1963e96adabc3287386006
x64

### Steps to Reproduce

- Run code-server 0.103.0+.
- Install Copilot Chat extension (0.30+ can be installed from Marketplace, but not on 4.102.3 — only via VSIX).
- Try to use Copilot Chat (tested with 0.29.1 and 0.30+).

### Expected

- Copilot Chat should either:
- Continue working on 4.103.0+ as it did before, or
- Fail with a clear error instead of hanging.

### Actual

- On 4.103.0+, Copilot Chat 0.29.1 no longer works:
- No requests go through.
- Output panel does not show fetched model metadata.
- Copilot Chat displays "Working..." indefinitely.

### Logs

```shell

```

### Screenshot/Video

_No response_

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

I did not test native VS Code

### 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

_No response_