Backport: feat(openai): add o3-deep-research and o4-mini-deep-research models (#10034)

This is an automated backport of #10033 to the release-v5.0 branch.

Co-authored-by: Gregor Martynus <39992+gr2m@users.noreply.github.com>

Author: vercel-ai-sdk[bot]

.changeset/rich-rivers-visit.md

@@ -0,0 +1,5 @@
+---
+'@ai-sdk/openai': patch
+---
+
+feat(openai): add `o3-deep-research` and `o4-mini-deep-research` models

packages/openai/src/responses/openai-responses-options.ts

@@ -17,12 +17,16 @@ export const TOP_LOGPROBS_MAX = 20;
 export const openaiResponsesReasoningModelIds = [
   'o1',
   'o1-2024-12-17',
-  'o3-mini',
-  'o3-mini-2025-01-31',
   'o3',
   'o3-2025-04-16',
+  'o3-deep-research',
+  'o3-deep-research-2025-06-26',
+  'o3-mini',
+  'o3-mini-2025-01-31',
   'o4-mini',
   'o4-mini-2025-04-16',
+  'o4-mini-deep-research',
+  'o4-mini-deep-research-2025-06-26',
   'codex-mini-latest',
   'computer-use-preview',
   'gpt-5',