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/main.py

@@ -6,6 +6,7 @@ load_dotenv()  # load .env before db.py reads DATABASE_URL
 
 from fastapi import FastAPI  # noqa: E402
 from fastapi.middleware.cors import CORSMiddleware  # noqa: E402
+from fastmcp.utilities.lifespan import combine_lifespans  # noqa: E402
 
 from db import create_db_and_tables  # noqa: E402
 from innercontext.api import (  # noqa: E402
@@ -15,6 +16,9 @@ from innercontext.api import (  # noqa: E402
     routines,
     skincare,
 )
+from innercontext.mcp_server import mcp  # noqa: E402
+
+mcp_app = mcp.http_app(path="/mcp")
 
 
 @asynccontextmanager
@@ -23,7 +27,11 @@ async def lifespan(app: FastAPI):
     yield
 
 
-app = FastAPI(title="innercontext API", lifespan=lifespan, redirect_slashes=False)
+app = FastAPI(
+    title="innercontext API",
+    lifespan=combine_lifespans(lifespan, mcp_app.lifespan),
+    redirect_slashes=False,
+)
 
 app.add_middleware(
     CORSMiddleware,  # ty: ignore[invalid-argument-type]
@@ -39,6 +47,9 @@ app.include_router(routines.router, prefix="/routines", tags=["routines"])
 app.include_router(skincare.router, prefix="/skincare", tags=["skincare"])
 
 
+app.mount("/mcp", mcp_app)
+
+
 @app.get("/health-check")
 def health_check():
     return {"status": "ok"}