/clear and /restart breaks mcp integration

/clear and /restart leave MCP tools broken; only /mcp reload recovers them

Description

After running /clear (and also /restart), MCP tools stop working correctly in the new session. Restarting the CLI process from scratch (full exit + relaunch) works fine, so the issue is isolated to in-process session/state carryover — not the MCP server config itself. Running /mcp reload after /clear or /restart fixes it without needing a full process exit.

Steps to reproduce

1. Start a session with MCP servers configured and working.
2. Use MCP tools normally — confirm they work.
3. Run /clear.
4. Try to use an MCP tool — it fails / tools are unavailable.
5. Run /restart — issue persists.
6. Run /mcp reload — MCP tools work again.
7. Alternatively, fully exit and relaunch the CLI — works fine on first try.

Expected behavior

/clear and /restart should leave MCP tools in the same working state as a fresh CLI launch, without requiring a manual /mcp reload.

Environment

• Copilot CLI version: 1.0.83
• OS: Linux
• Related: possibly same root cause as #4697 (/clear doesn't terminate previous stdio MCP server child processes)

Start by tracing the /clear, /restart, and /mcp reload command handling and the in-process MCP session/state lifecycle described here. Compare those paths with a fresh CLI launch and the related issue #4697; done means MCP tools remain available after /clear and /restart without requiring /mcp reload.