feat: add streamable-http MCP transport alongside SSE

SSE transport has reliability issues through Cloudflare/Traefik proxies
(connections drop, causing init failures on reconnect). Streamable HTTP
is stateless — each request carries its own session, avoiding persistent
connection issues.

New endpoint: POST/GET/DELETE /mcp/mcp (streamable-http)
Existing: GET /mcp/sse + POST /mcp/messages/ (SSE, unchanged)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/claude_memory/api/app.py

@@ -15,6 +15,7 @@ from fastapi.responses import Response
 from fastapi.staticfiles import StaticFiles
 from mcp.server.fastmcp import FastMCP
 from mcp.server.sse import SseServerTransport
+from mcp.server.streamable_http import StreamableHTTPServerTransport
 from starlette.routing import Mount, Route
 from starlette.types import ASGIApp, Receive, Scope, Send
 
@@ -1296,11 +1297,57 @@ class HandleSSE:
             )
 
 
+# Streamable HTTP transport — stateless, no persistent SSE connection needed.
+# Each request carries its own init+tool call. More reliable through proxies.
+class HandleStreamableHTTP:
+    """ASGI app for streamable-http MCP connections."""
+    def __init__(self) -> None:
+        self._transport: StreamableHTTPServerTransport | None = None
+
+    async def __call__(self, scope: Any, receive: Any, send: Any) -> None:
+        user_id = "default"
+        for name, value in scope.get("headers", []):
+            if name == b"authorization":
+                token = value.decode().removeprefix("Bearer ").strip()
+                resolved = _resolve_user_from_token(token)
+                if resolved:
+                    user_id = resolved
+                break
+        _current_user.set(user_id)
+
+        session_id = None
+        for name, value in scope.get("headers", []):
+            if name == b"mcp-session-id":
+                session_id = value.decode()
+                break
+
+        transport = StreamableHTTPServerTransport(
+            mcp_session_id=session_id,
+            is_json_response_enabled=True,
+        )
+        async with transport.connect() as (read_stream, write_stream):
+            import anyio
+            async with anyio.create_task_group() as tg:
+                async def run_server() -> None:
+                    await mcp_server._mcp_server.run(
+                        read_stream, write_stream,
+                        mcp_server._mcp_server.create_initialization_options(),
+                    )
+
+                tg.start_soon(run_server)
+                await transport.handle_request(scope, receive, send)
+                tg.cancel_scope.cancel()
+
+
+streamable_handler = HandleStreamableHTTP()
+
 # Static files for UI (before MCP mount)
 app.mount("/static", StaticFiles(directory=UI_DIR), name="static")
 
-# Client connects to /mcp/sse, posts to /mcp/messages/
+# Client connects to /mcp/sse, posts to /mcp/messages/ (SSE transport)
+# Client can also POST to /mcp/mcp (streamable-http transport)
 app.router.routes.insert(0, Mount("/mcp", routes=[
     Route("/sse", endpoint=HandleSSE()),
     Mount("/messages", app=sse_transport.handle_post_message),
+    Route("/mcp", endpoint=streamable_handler, methods=["GET", "POST", "DELETE"]),
 ]))