feat(responses): respect client streaming preference + string input support (#121)

- Remove forced stream=true from responsesHandler
- Add stream-to-JSON converter for non-streaming clients (Codex)
- Accept string input in Responses API (normalize to array)
- Codex SSE header fallback for missing Content-Type
- Refactor: extract shared normalizeResponsesInput()

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>
Co-authored-by: Cursor <cursoragent@cursor.com>

open-sse/services/provider.js

@@ -36,8 +36,9 @@ function buildAnthropicCompatibleUrl(baseUrl) {
 
 // Detect request format from body structure
 export function detectFormat(body) {
-  // OpenAI Responses API: has input[] array instead of messages[]
-  if (body.input && Array.isArray(body.input)) {
+  // OpenAI Responses API: has input (array or string) instead of messages[]
+  // The Responses API accepts both input as array and input as a plain string
+  if (body.input && (Array.isArray(body.input) || typeof body.input === "string") && !body.messages) {
     return "openai-responses";
   }