feat: surface MCP server status in System Status page

Add per-tool in-memory call counters to the MCP module and a
GET /api/v1/status/mcp endpoint that joins them with the live tool
registry and endpoint config, then render it as a new card on the
System Status page with a one-click client-config copy button.

- app/mcp/stats.py: lock-guarded MCPStatsTracker (the mcp SDK runs sync
  tool bodies via anyio.to_thread.run_sync, so this is genuinely
  multi-threaded, unlike the async REST routes)
- app/mcp/server.py: instrument search_regulations, add get_mcp_status()
- app/config/settings.py: optional MCP_PUBLIC_URL override, required
  because the Vite proxy and reverse proxies rewrite the Host header
- StatusPage.tsx: MCP Server card, joins the existing parallel fetch

Counters are process-local by design; token usage is already persisted
by ModelUsageTracker since MCP calls route through ask().

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/app/api/routes/status.py

@@ -4,10 +4,11 @@ import asyncio
 import time
 from typing import Any
 
-from fastapi import APIRouter
+from fastapi import APIRouter, Request
 
 from app.config.settings import settings
 from app.domain.retrieval import RetrievedChunk
+from app.mcp.server import get_mcp_status
 from app.services.llm.llm_factory import get_llm_client, get_llm_factory
 from app.shared.bootstrap import (
     get_bm25_retriever,
@@ -280,3 +281,17 @@ async def ping_model_connections():
     ]
     await asyncio.gather(*tasks, return_exceptions=True)
     return {"models": [_build_model_status(role) for role in _MODEL_ROLES]}
+
+
+@router.get("/mcp")
+async def get_mcp_server_status(request: Request):
+    """Return MCP endpoint config, advertised tools, and per-tool call counters.
+
+    This route is a thin HTTP adapter: everything MCP-specific is assembled by
+    app.mcp.server.get_mcp_status(). The only thing decided here is the public
+    URL, because only the HTTP layer knows how the client reached us.
+    """
+    # request.base_url already carries scheme/host/port and a trailing slash;
+    # strip it before appending so the result is ".../mcp/", not ".../mcp//".
+    public_url = settings.mcp_public_url or f"{str(request.base_url).rstrip('/')}/mcp/"
+    return await get_mcp_status(public_url)