[codex] Use input items for Responses Lite tools (#27946)

When using Responses Lite, we should all use `additional_tools` and a
developer item instead of the top level tools array & instructions
field. This keeps things 1-to-1.

Forced namespacing for _all_ tools will land in a following PR after
some coordination & fixes in Responses API (around collisions & return
items).

The goal is to eventually expand the scope of this to _all_ requests
from codex, but that will require larger coordination across providers &
slower rollout.

codex-rs/codex-api/src/endpoint/responses_websocket.rs

@@ -838,11 +838,11 @@ mod tests {
                 phase: None,
                 internal_chat_message_metadata_passthrough: None,
             }],
-            tools: vec![json!({
+            tools: Some(vec![json!({
                 "type": "function",
                 "name": "lookup",
                 "parameters": {"type": "object"}
-            })],
+            })]),
             tool_choice: "auto".to_string(),
             parallel_tool_calls: true,
             reasoning: None,