[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/core/src/turn_timing.rs

@@ -380,7 +380,8 @@ fn response_item_records_turn_ttft(item: &ResponseItem) -> bool {
         | ResponseItem::Compaction { .. }
         | ResponseItem::ContextCompaction { .. } => true,
         ResponseItem::CompactionTrigger { .. } => false,
-        ResponseItem::FunctionCallOutput { .. }
+        ResponseItem::AdditionalTools { .. }
+        | ResponseItem::FunctionCallOutput { .. }
         | ResponseItem::CustomToolCallOutput { .. }
         | ResponseItem::ToolSearchOutput { .. }
         | ResponseItem::Other => false,