Client ID Metadata Documents support

### Describe the feature or problem you’d like to solve

[Client ID Metadata Documents](https://modelcontextprotocol.io/specification/2026-07-28/basic/authorization/client-registration#client-id-metadata-documents) are the new standard way to authorize through OAuth, without preregistering a client. My organization disallows using PAT's for our private repositories as they give too much access and they can't control who can make PAT's. Fine grained access tokens are not supported by the MCP, so OAuth is the next step.

### Proposed solution

The MCP Server can be used by way more clients than Visual Studio Code and Copilot CLI alone, expanding the usefulness of the MCP server over using the `gh` CLI.

### Example prompts or workflows (for tools/toolsets only)

N/A

### Additional context

Add any other context like screenshots or mockups are helpful, if applicable.

Start by reading the linked Client ID Metadata Documents specification and reviewing the MCP server's existing OAuth authorization flow. Done means clients can authorize through OAuth without preregistration, with support extending beyond Visual Studio Code and Copilot CLI.

Written by the indexing model from the issue text.