feat(mcp): add FastMCP server with 14 tools for LLM agent access

- Add backend/innercontext/mcp_server.py with tools covering products,
  inventory, routines, skin snapshots, medications, lab results, and
  grooming schedule
- Mount MCP app at /mcp in main.py using combine_lifespans
- Fix test isolation: patch app.router.lifespan_context in conftest to
  avoid StreamableHTTPSessionManager single-run limitation

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/tests/conftest.py

@@ -1,4 +1,5 @@
 import os
+from contextlib import asynccontextmanager
 
 # Must be set before importing db (which calls create_engine at module level)
 os.environ.setdefault("DATABASE_URL", "sqlite://")
@@ -13,6 +14,18 @@ from db import get_session
 from main import app
 
 
+@asynccontextmanager
+async def _db_only_lifespan(a):
+    """Lifespan without the MCP server for test isolation.
+
+    StreamableHTTPSessionManager.run() can only be called once per instance,
+    which conflicts with the per-test TestClient lifecycle. We replace the
+    combined (db + MCP) lifespan with one that only does DB setup.
+    """
+    db_module.create_db_and_tables()
+    yield
+
+
 @pytest.fixture()
 def session(monkeypatch):
     """Per-test fresh SQLite in-memory database with full isolation."""
@@ -32,8 +45,11 @@ def session(monkeypatch):
 
 
 @pytest.fixture()
-def client(session):
+def client(session, monkeypatch):
     """TestClient using the per-test session for every request."""
+    # Replace combined (db+MCP) lifespan with DB-only to avoid the
+    # StreamableHTTPSessionManager single-run limitation.
+    monkeypatch.setattr(app.router, "lifespan_context", _db_only_lifespan)
 
     def _override():
         yield session