Can't use BYOK when github copilot is down.

Does this issue occur when all extensions are disabled?: Yes/No

- VS Code Version:
- OS Version:

Steps to Reproduce:

1. use BYOK model. Try it in GitHub Copilot. You will see the screenshot I attached

2. You will be logged you out because GitHub login API returns 503.

Based on my understanding, the current VS Code architecture initiates requests from the user's machine, not directly from the GitHub Copilot server.

The communication from the GitHub server would make sense if the model were GitHub Copilot's proprietary one. However, I am currently unable to use GitHub Copilot (free tier) because GitHub returns a 503 error when the service is unavailable.

I believe that in such situations, users should be allowed to use their own Bring Your Own Key (BYOK) solutions. The last time GitHub Copilot experienced an outage, I was unable to use the service.

Could this be addressed? I've encountered GitHub Copilot being down twice in the past two to three weeks. Allowing users to utilize BYOK in these instances would prevent complete service interruption."