Use session IDs for prompt cache keys (#33035)

## What changed

- Default `prompt_cache_key` to the session ID from response metadata instead of the thread ID.
- Preserve explicit prompt cache key overrides.
- Verify that API-key-authenticated root and subagent requests use the same session-based cache key even though they have different thread IDs.

GitOrigin-RevId: cb1bf21a3cb8fa2c5083c5c6afd4829ff2adcf1f

codex-rs/core/src/client.rs

@@ -466,10 +466,10 @@ impl ModelClient {
         self
     }
 
-    fn prompt_cache_key(&self) -> String {
+    fn prompt_cache_key(&self, responses_metadata: &CodexResponsesMetadata) -> String {
         self.prompt_cache_key_override
             .clone()
-            .unwrap_or_else(|| self.state.thread_id.to_string())
+            .unwrap_or_else(|| responses_metadata.session_id.clone())
     }
 
     /// Creates a fresh turn-scoped streaming session.
@@ -885,7 +885,7 @@ impl ModelClient {
             &prompt.output_schema,
             prompt.output_schema_strict,
         );
-        let prompt_cache_key = Some(self.prompt_cache_key());
+        let prompt_cache_key = Some(self.prompt_cache_key(responses_metadata));
         let service_tier = model_info.service_tier_for_request(service_tier);
         let request = ResponsesApiRequest {
             model: model_info.slug.clone(),