fix(openai): omit reasoning item id when store is false

[giulio-leone]

Summary

Fixes #12687

Azure OpenAI rejects reasoning items that include an id field when store is disabled.

Root Cause

In convert-to-openai-responses-input.ts, the store: false branch for reasoning messages was creating objects with id: reasoningId:

reasoningMessages[reasoningId] = {
  type: 'reasoning',
  id: reasoningId,          // ← Azure rejects this when store=false
  encrypted_content: ...,
  summary: summaryParts,
};

The store: true branch correctly uses item_reference with id (line 384). But when store is false, the reasoning content should be sent inline without an id — the same pattern used for reasoning without an itemId (lines 450-454).

Fix

Remove id: reasoningId from the reasoning message object created in the store: false path. The reasoningId is still used as the local tracking key in reasoningMessages for deduplication, but it is not sent to the API.

594/594 OpenAI provider tests pass (2 consecutive clean runs).

[giulio-leone]

Intervention note for this PR:

Current blocker appears to be Vercel deployment authorization, not code/test correctness.

Observed pattern:

• Vercel check fails with: "Authorization required to deploy."
• Other checks (e.g., Socket Security / Vercel Agent Review) are passing.

Recommended unblock sequence:

1. Complete the Vercel Git authorization flow from the failing check link.
2. Re-run checks on this PR.
3. If Vercel passes, this PR should move forward with normal review.

If useful, I can follow up with a PR-by-PR status sweep after authorization is completed.

[giulio-leone]

This PR is ready for review — all CI checks pass, no merge conflicts, and all review threads have been resolved. Ready to merge when approved. 🚀