Constantly encountered 'Authorization error, you may need to run /login'

### Describe the bug

I have already logined, but constantly encountered 'Authorization error, you may need to run /login'

```
No copilot instructions found. Run /init to generate a copilot-instructions.md file for this project.

! Failed to load 1 skill. Run /skills for more details.

● Welcome shayne-snap!

! MCP server 'github-mcp-server' is taking longer than expected to connect.

! Failed to connect to MCP server 'github-mcp-server'. Execute '/mcp show github-mcp-server' to inspect or check the logs.

● Environment loaded: 2 skills

✗ Authorization error, you may need to run /login (Request ID: E959:39D085:5B45AD:6B5594:69DDA4E1)

! Failed to connect to MCP server 'github-mcp-server'. Execute '/mcp show github-mcp-server' to inspect or check the logs.

● GitHub MCP Server: Connected

● You have been logged out successfully.

! Failed to connect to MCP server 'github-mcp-server'. Execute '/mcp show github-mcp-server' to inspect or check the logs.

● MCP Servers reloaded: 0 servers connected

! Failed to connect to MCP server 'github-mcp-server'. Execute '/mcp show github-mcp-server' to inspect or check the logs.

● GitHub MCP Server: Connected

● Signed in successfully as shayne-snap!

! Failed to connect to MCP server 'github-mcp-server'. Execute '/mcp show github-mcp-server' to inspect or check the logs.

● MCP Servers reloaded: 0 servers connected

✗ Authorization error, you may need to run /login (Request ID: E959:39D085:5C765C:6CB527:69DDA53C)

● Welcome shayne-snap!

```

### Affected version

GitHub Copilot CLI 1.0.25

### Steps to reproduce the behavior

_No response_

### Expected behavior

_No response_

### Additional context

MacOS

uname -a
Darwin MacBook-Pro.local 25.0.0 Darwin Kernel Version 25.0.0: Mon Aug 25 21:17:53 PDT 2025; root:xnu-12377.1.9~3/RELEASE_ARM64_T8112 arm64

Start by reproducing the failure on macOS with GitHub Copilot CLI 1.0.25, then inspect the `/login` flow and `/mcp show github-mcp-server` output and logs. Determine why authentication fails after a reported successful sign-in, and verify that the authorization error no longer recurs during MCP connection and reload operations.

索引モデルが issue の本文から書いたものです。