Fix GPT-5 Responses API issues with condensing and image support

- Fix manual condensing bug by setting skipPrevResponseIdOnce flag in Task.ts
- Revert to string-based format for full conversations after condensing
- Add proper image support with structured format when using previous_response_id
- Update test suite to match new implementation where all models use Responses API
- Handle 400 errors gracefully when previous_response_id is not found

Fixes issues introduced in PR #6864

Author: daniel-lxs

src/api/index.ts

@@ -52,6 +52,11 @@ export interface ApiHandlerCreateMessageMetadata {
 	 * Used to enforce "skip once" after a condense operation.
 	 */
 	suppressPreviousResponseId?: boolean
+	/**
+	 * Controls whether the response should be stored for 30 days (OpenAI Responses API).
+	 * Defaults to true if not specified.
+	 */
+	store?: boolean
 }
 
 export interface ApiHandler {