claude mcp add during a running session doesn't appear in /mcp until a new session starts

What happened

Ran claude mcp add --transport http smartbear-bugsnag https://bugsnag.mcp.smartbear.com/mcp -s user from a shell while a Claude Code session was already open. It wrote the server to ~/.claude.json, and a fresh claude mcp list shows it. But in the session that was already running, /mcp never lists the new server. Opening a brand-new session shows it fine.

Expected

/mcp in the running session reflects the updated config (or exposes a reload/reconnect action), without needing to start a new session.

Actual

The running session's MCP server list is fixed at startup; config changes made via claude mcp add are invisible to that session's /mcp until it is restarted.

Repro

1. Start a Claude Code session.
2. In another shell, run claude mcp add --transport http <name> <url> -s user.
3. Confirm claude mcp list shows it.
4. In the original session, run /mcp -> the new server is absent.
5. Start a new session, run /mcp -> it appears.

100% reproducible.

Environment

• Claude Code, macOS (darwin).
• Server added at user scope (-s user), HTTP transport.