feat(openai): Set gen_ai.tool.definitions for the Responses API

[alexander-alderman-webb]

Description

Set the attribute according to the schema defined in

https://github.com/getsentry/rfcs/blob/main/text/0153-decoupling-sentrys-generative-ai-conventions-from-open-telemetry.md

Issues

Closes #5762

Reminders

• Please add tests to validate your changes, and lint your code using uv run ruff.
• Add GH Issue ID & Linear ID (if applicable)
• PR title should use conventional commit style (feat:, fix:, ref:, meta:)
• For external contributors: CONTRIBUTING.md, Sentry SDK development docs, Discord community

[github-actions]

Codecov Results 📊

✅ 99634 passed | ⏭️ 6757 skipped | Total: 106391 | Pass Rate: 93.65% | Execution Time: 349m 3s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +80
Passed Tests	📈 +56
Failed Tests	—
Skipped Tests	📈 +24

All tests are passing successfully.

✅ Patch coverage is 93.75%. Project has 2502 uncovered lines.
✅ Project coverage is 89.89%. Comparing base (base) to head (head).

Files with missing lines (1)

File	Patch %	Lines
sentry_sdk/ai/_openai_responses_api.py	92.86%	⚠️ 2 Missing and 7 partials

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    89.87%    89.89%    +0.02%
==========================================
  Files          193       193         —
  Lines        24719     24747       +28
  Branches      8838      8858       +20
==========================================
+ Hits         22215     22245       +30
- Misses        2504      2502        -2
- Partials      1410      1413        +3

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