[BUG] Claude Code sends ~20 tools/list requests on a single MCP connection and accumulates tools (8 → 160)

Title:
Claude Code sends ~20 tools/list requests on a single MCP connection and accumulates tools (8 → 160)

Body:
### What happened

On connecting to a remote MCP server, Claude Code issues ~20 tools/list
requests within ~5 seconds of a single connection, and accumulates the
results in the tool list instead of replacing. The server exposes 8 tools, but
Claude Code's /mcp panel shows 160 (8 × ~20).

### Environment

• Claude Code: 2.1.218 (latest; claude update reports up to date)
• OS: macOS
• MCP server: stdio server wrapped by mcp-proxy 0.12.0, behind nginx
• Transport: reproduced on both --transport http (streamable-http) and

--transport sse; and with mcp-proxy both stateful and --stateless

• Server capability: capabilities.tools.listChanged = false

(so this is NOT notification-driven)

### Steps to reproduce

1. Run any MCP server behind mcp-proxy (streamable-http /mcp endpoint).

Server returns 8 tools for tools/list.

1. claude mcp add --transport http <name> https://<host>/<path>/mcp --header "Authorization: Bearer <token>"
2. Open Claude Code, connect the server, open /mcp.

### Expected

Fetch tools/list once per connection (or replace on refresh). Show 8 tools.

### Actual

Claude Code sends ~20 tools/list in one connect and shows 8 × 20 = 160 tools
(the 8 tool names repeated ~20 times).

### Evidence (server access log, one Claude Code connect)

POST /mcp 200 (initialize)
POST /mcp 202 (notifications/initialized)
GET /mcp 200 (open stream)
POST /mcp 200 method=tools/list <-- repeated ~20x within ~5s
POST /mcp 200 method=tools/list
... (about 20 times) ...

### Cross-check (server is correct)

• curl calling tools/list directly returns 8 tools (once).
• Codex connecting to the SAME endpoint shows the correct 8 tools.
• Reproduced on 3 different Macs, fresh windows/conversations.

So the server + proxy return 8 correctly; only Claude Code inflates to 160.