Avoid rendering generated images twice (#34378)

## What changed

- Tell the model that generated images are already displayed to the user and should not be repeated as Markdown images or file links.
- Keep generated-image artifact paths and output hints owned by the image generation extension.
- Centralize the availability check for the image generation tool across feature, provider, namespace-tool, model modality, and authentication requirements.

## Testing

- Verify artifact paths sanitize session and call identifiers.
- Verify the model-facing output hint reports that the generated image is already displayed.

GitOrigin-RevId: 6c865b6a96d6a71bb2c33246d1518a00e7c8b840

codex-rs/ext/image-generation/src/tool.rs

@@ -8,8 +8,6 @@ use codex_api::ImageEditRequest;
 use codex_api::ImageGenerationRequest;
 use codex_api::ImageQuality;
 use codex_api::ImageUrl;
-use codex_core::context::extension_image_generation_output_hint;
-use codex_core::image_generation_artifact_path;
 use codex_exec_server::CreateDirectoryOptions;
 use codex_exec_server::ExecutorFileSystem;
 use codex_exec_server::LOCAL_FS;
@@ -52,6 +50,8 @@ use serde_json::Value;
 
 use crate::IMAGE_GEN_NAMESPACE;
 use crate::IMAGEGEN_TOOL_NAME;
+use crate::artifact::image_generation_artifact_path;
+use crate::artifact::image_generation_output_hint;
 use crate::backend::CodexImagesBackend;
 
 const IMAGE_MODEL: &str = "gpt-image-2";
@@ -217,7 +217,7 @@ impl ImageGenerationTool {
             .await;
         let output_hint = saved_path.as_ref().and_then(|output_path| {
             let output_dir = output_path.parent()?;
-            extension_image_generation_output_hint(output_dir.display(), output_path.display())
+            image_generation_output_hint(output_dir.display(), output_path.display())
         });
         Ok(Box::new(GeneratedImageOutput {
             result,