[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/tests/clients.rs

@@ -315,7 +315,7 @@ async fn responses_client_stream_request_preserves_item_ids() -> Result<()> {
             phase: None,
             internal_chat_message_metadata_passthrough: None,
         }],
-        tools: Vec::new(),
+        tools: Some(Vec::new()),
         tool_choice: "auto".into(),
         parallel_tool_calls: false,
         reasoning: None,
@@ -401,7 +401,7 @@ async fn streaming_client_retries_on_transport_error() -> Result<()> {
         model: "gpt-test".into(),
         instructions: "Say hi".into(),
         input: Vec::new(),
-        tools: Vec::new(),
+        tools: Some(Vec::new()),
         tool_choice: "auto".into(),
         parallel_tool_calls: false,
         reasoning: None,
@@ -520,7 +520,7 @@ async fn azure_store_sends_ids_and_headers() -> Result<()> {
             phase: None,
             internal_chat_message_metadata_passthrough: None,
         }],
-        tools: Vec::new(),
+        tools: Some(Vec::new()),
         tool_choice: "auto".into(),
         parallel_tool_calls: false,
         reasoning: None,