[BUG] /mcp dialog hides servers with zero tools, blocking mid-session reconnect

Summary

When a remote HTTP MCP server connects successfully but returns zero tools from tools/list (e.g. due to a network blip at session startup), the /mcp dialog does not show that server at all. This makes it impossible to manually reconnect or re-probe the server mid-session, leaving the user with no recovery path short of /clear and losing conversation context.

Steps to reproduce

1. Start a Claude Code session with one or more remote HTTP MCP servers configured (e.g. claude.ai Datadog, claude.ai Atlassian).
2. Have a brief network interruption at session startup so that the tools/list probe fails silently — the server will still show ✓ Connected in claude mcp list because the OAuth token check succeeds, but the tool schemas were never registered.
3. Open the /mcp dialog.

Expected behavior

The /mcp dialog shows all registered MCP servers, regardless of how many tools they returned. Servers in a "connected but zero tools" state should be visible and offer a Reconnect option to re-run tools/list.

Actual behavior

The /mcp dialog only shows servers that have at least one registered tool. Servers in the "connected + zero tools" state are completely hidden from the dialog, so there is no UI path to reconnect them.

Why this matters

This compounds an existing startup reliability issue with remote HTTP MCPs:

1. Network blip at startup → tools/list probe fails silently → zero tools registered (related: #55914, #42148)
2. /mcp dialog hides the server → no reconnect path → user is stuck for the entire session

The two bugs together make the "connected but no tools" state unrecoverable without losing context. Fixing the dialog to show all registered servers (filtering by tool count for display purposes only, not for visibility) would restore the manual recovery path even while the underlying startup reliability issue is separately addressed.

Environment

• Platform: macOS
• Claude Code CLI
• Remote HTTP MCP servers via claude.ai integration (OAuth)

Workaround

None available mid-session. User must start a new session and hope the network is stable at startup.

— Claude Sonnet 4.6 on behalf of @tmeneau