fix: serve MCP over Streamable HTTP instead of legacy SSE

Current MCP clients (OpenCode, Claude, ...) only speak Streamable HTTP: they
POST JSON-RPC to the configured URL, so a legacy SSE endpoint answers
405 Method Not Allowed and not a single tool can be reached.

Run FastMCP's http_app (build_app()) under uvicorn instead of mcp.run(sse):
the MCP endpoint is now /mcp, and the custom GET /health route keeps serving
the Kubernetes probes.

Add transport tests asserting /mcp and /health are exposed and /sse is gone.

src/server.py

@@ -9,6 +9,7 @@ from typing import Any, Optional
 import qdrant_client as qdrant_pkg
 from dateutil import parser as date_parser
 from email.utils import parseaddr
+import uvicorn
 from dotenv import load_dotenv
 from starlette.requests import Request
 from starlette.responses import JSONResponse
@@ -340,6 +341,23 @@ def read_email(message_id: str):
         return {"error": f"read_email failed: {exc}"}
 
 
+# Streamable HTTP is the transport supported by current MCP clients (OpenCode,
+# Claude, ...). The legacy SSE transport is deprecated and is also a POST
+# target for clients that only speak Streamable HTTP, which answers 405.
+MCP_HOST = "0.0.0.0"
+MCP_PORT = 8000
+MCP_HTTP_PATH = "/mcp"
+
+
+def build_app():
+    """Builds the ASGI app serving the MCP endpoint over Streamable HTTP.
+
+    The MCP endpoint lives at MCP_HTTP_PATH; the custom route declared above
+    keeps serving GET /health for the Kubernetes probes.
+    """
+    return mcp.http_app(path=MCP_HTTP_PATH)
+
+
 if __name__ == "__main__":
     logger.info("Initializing models before starting server...")
     try:
@@ -347,7 +365,6 @@ if __name__ == "__main__":
         logger.info("Models loaded successfully.")
     except Exception as e:
         logger.error(f"Failed to load models: {e}")
-    
-    logger.info("Starting SSE server on 0.0.0.0:8000...")
-    # Start the MCP server using SSE (Server-Sent Events) over HTTP
-    mcp.run(transport="sse", host="0.0.0.0", port=8000)
+
+    logger.info(f"Starting Streamable HTTP server on {MCP_HOST}:{MCP_PORT}{MCP_HTTP_PATH}...")
+    uvicorn.run(build_app(), host=MCP_HOST, port=MCP_PORT)