feat(openai-agents): Inject propagation headers for HostedMCPTool

[alexander-alderman-webb]

Description

Add sentry-trace and baggage to headers field of hosted tool definitions sent to the OpenAI responses API.

• Factor out logic to prevent duplicate Sentry baggage from the httpx integration.
• Inject headers in the patch for the wrapper of the HTTP call to OpenAI responses API.

Issues

Closes PY-1993

Reminders

• Please add tests to validate your changes, and lint your code using tox -e linters.
• 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]

Semver Impact of This PR

🟡 Minor (new features)

📋 Changelog Preview

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New Features ✨

• feat(asyncio): Add on-demand way to enable AsyncioIntegration by sentrivana in #5288

• feat(openai-agents): Inject propagation headers for HostedMCPTool by alexander-alderman-webb in #5297

Bug Fixes 🐛

• fix(ai): redact message parts content of type blob by constantinius in #5243
• fix(clickhouse): Guard against module shadowing by alexander-alderman-webb in #5250
• fix(gql): Revert signature change of patched gql.Client.execute by alexander-alderman-webb in #5289
• fix(litellm): Guard against module shadowing by alexander-alderman-webb in #5249
• fix(pure-eval): Guard against module shadowing by alexander-alderman-webb in #5252
• fix(ray): Guard against module shadowing by alexander-alderman-webb in #5254
• fix(threading): Handle channels shadowing by sentrivana in #5299
• fix(typer): Guard against module shadowing by alexander-alderman-webb in #5253

Documentation 📚

• docs: Update Python versions banner in README by sentrivana in #5287

Internal Changes 🔧

• chore(gen_ai): add auto-enablement for google genai by shellmayr in #5295
• ci(release): Switch from action-prepare-release to Craft by BYK in #5290

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[linear]

PY-1993 AI Integration -> MCP trace propagation