core: strip image detail from Responses Lite requests (#27246)

## Summary

- Strip image `detail` fields from every Responses Lite request.
- Apply stripping to message images and function/custom tool-output
images.
- Transform only the formatted request copy without mutating stored
history.
- Preserve image URLs byte-for-byte, including HTTP(S) URLs, without
downloading, validating, or resizing them.
- Preserve all image `detail` fields for non-Responses-Lite models.

## Motivation

Responses Lite does not support image `detail` tags, so Codex must omit
them whenever `model_info.use_responses_lite` is enabled. This transport
requirement is independent of the `resize_all_images` feature.

Stored history retains the original detail values. This keeps
request-specific formatting isolated from conversation state and
preserves the information for local image preparation and
non-Responses-Lite requests.


#### [git stack](https://github.com/magus/git-stack-cli)
- ✅ `1` https://github.com/openai/codex/pull/27245
- ✅ `2` https://github.com/openai/codex/pull/27247
- 👉 `3` https://github.com/openai/codex/pull/27246
- ⏳ `4` https://github.com/openai/codex/pull/27266

codex-rs/core/src/client_common.rs

@@ -2,6 +2,8 @@ pub use codex_api::ResponseEvent;
 use codex_config::types::Personality;
 use codex_protocol::error::Result;
 use codex_protocol::models::BaseInstructions;
+use codex_protocol::models::ContentItem;
+use codex_protocol::models::FunctionCallOutputContentItem;
 use codex_protocol::models::ResponseItem;
 use codex_protocol::protocol::InterAgentCommunication;
 use codex_tools::ToolSpec;
@@ -71,6 +73,56 @@ impl Prompt {
             })
             .collect()
     }
+
+    pub(crate) fn get_formatted_input_for_request(
+        &self,
+        use_responses_lite: bool,
+    ) -> Vec<ResponseItem> {
+        let mut input = self.get_formatted_input();
+        if use_responses_lite {
+            strip_image_details(&mut input);
+        }
+        input
+    }
+}
+
+fn strip_image_details(items: &mut [ResponseItem]) {
+    for item in items {
+        match item {
+            ResponseItem::Message { content, .. } => {
+                for content_item in content {
+                    if let ContentItem::InputImage { detail, .. } = content_item {
+                        *detail = None;
+                    }
+                }
+            }
+            ResponseItem::FunctionCallOutput { output, .. }
+            | ResponseItem::CustomToolCallOutput { output, .. } => {
+                if let Some(content) = output.content_items_mut() {
+                    for content_item in content {
+                        if let FunctionCallOutputContentItem::InputImage { detail, .. } =
+                            content_item
+                        {
+                            *detail = None;
+                        }
+                    }
+                }
+            }
+            ResponseItem::Reasoning { .. }
+            | ResponseItem::AgentMessage { .. }
+            | ResponseItem::LocalShellCall { .. }
+            | ResponseItem::FunctionCall { .. }
+            | ResponseItem::ToolSearchCall { .. }
+            | ResponseItem::CustomToolCall { .. }
+            | ResponseItem::ToolSearchOutput { .. }
+            | ResponseItem::WebSearchCall { .. }
+            | ResponseItem::ImageGenerationCall { .. }
+            | ResponseItem::Compaction { .. }
+            | ResponseItem::CompactionTrigger
+            | ResponseItem::ContextCompaction { .. }
+            | ResponseItem::Other => {}
+        }
+    }
 }
 
 pub struct ResponseStream {