test(mcp): add e2e test for stateless StreamableHTTP behavior (#22033)

Adds TestProxyMcpStatelessBehavior to test_proxy_mcp_e2e.py with a test
that verifies two independent MCP clients can connect, initialize, and
call tools without sharing session state. This catches the regression
from PR #19809 where stateless=False broke clients that don't manage
mcp-session-id headers.

Regression test for #20242

tests/mcp_tests/test_proxy_mcp_e2e.py

@@ -234,3 +234,62 @@ class TestProxyMcpSimpleConnections:
                     )
                     assert stdio_result == "5"
                     assert streamable_result == "9"
+
+
+class TestProxyMcpStatelessBehavior:
+    """
+    Verify that the LiteLLM MCP proxy operates in stateless mode.
+
+    When StreamableHTTPSessionManager is configured with stateless=True,
+    independent clients must be able to connect, list tools, and call tools
+    without sharing or inheriting session state from other clients.
+
+    With stateless=False this fails because the server tracks sessions and
+    expects clients to supply an mcp-session-id header obtained from a
+    prior handshake — breaking clients that don't manage session IDs.
+
+    Regression test for https://github.com/BerriAI/litellm/issues/20242
+    """
+
+    @pytest.mark.asyncio
+    async def test_independent_clients_no_shared_session(
+        self, proxy_server_url: str
+    ) -> None:
+        """Two independent clients connect and operate without sharing session state."""
+        async with asyncio.timeout(30):
+            # --- Client A: connect, initialize, call tool ---
+            async with streamablehttp_client(
+                url=f"{proxy_server_url}/mcp",
+                headers={
+                    "Authorization": PROXY_AUTHORIZATION_HEADER,
+                    "x-mcp-servers": "math_stdio",
+                },
+            ) as (read_a, write_a, _get_sid_a):
+                async with ClientSession(read_a, write_a) as session_a:
+                    await session_a.initialize()
+                    result_a = await session_a.call_tool(
+                        "add", arguments={"a": 10, "b": 20}
+                    )
+                    assert result_a.content
+                    text_a = getattr(result_a.content[0], "text", None)
+                    assert text_a == "30"
+
+            # --- Client B: completely independent connection ---
+            async with streamablehttp_client(
+                url=f"{proxy_server_url}/mcp",
+                headers={
+                    "Authorization": PROXY_AUTHORIZATION_HEADER,
+                    "x-mcp-servers": "math_stdio",
+                },
+            ) as (read_b, write_b, _get_sid_b):
+                async with ClientSession(read_b, write_b) as session_b:
+                    await session_b.initialize()
+                    tools = await session_b.list_tools()
+                    assert any(t.name.endswith("add") for t in tools.tools)
+                    result_b = await session_b.call_tool(
+                        "add", arguments={"a": 100, "b": 200}
+                    )
+                    assert result_b.content
+                    text_b = getattr(result_b.content[0], "text", None)
+                    assert text_b == "300"
+