fix(anthropic): Set exception info on streaming span when applicable

[alexander-alderman-webb]

Description

Consolidate span finishing code in the __exit__ block of a new _StreamSpanContext context manager.
Forward exception info from _StreamSpanContext.__exit__() to Span.__exit__().

Issues

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]

Codecov Results 📊

✅ 13 passed | Total: 13 | Pass Rate: 100% | Execution Time: 7.37s

All tests are passing successfully.

❌ Patch coverage is 0.00%. Project has 14347 uncovered lines.

Files with missing lines (1)

File	Patch %	Lines
anthropic.py	5.83%	⚠️ 404 Missing

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Generated by Codecov Action

[github-actions]

Semver Impact of This PR

🟢 Patch (bug fixes)

📋 Changelog Preview

This is how your changes will appear in the changelog.
Entries from this PR are highlighted with a left border (blockquote style).

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New Features ✨

• (logging) Separate ignore lists for events/breadcrumbs and sentry logs by sl0thentr0py in #5698

Bug Fixes 🐛

Anthropic

• Set exception info on streaming span when applicable by alexander-alderman-webb in #5683

• Patch AsyncStream.close() and AsyncMessageStream.close() to finish spans by alexander-alderman-webb in #5675
• Patch Stream.close() and MessageStream.close() to finish spans by alexander-alderman-webb in #5674

Documentation 📚

• Add note on AI PRs to CONTRIBUTING.md by sentrivana in #5696

Internal Changes 🔧

• Add client report tests for span streaming by sentrivana in #5677

Other

• Update CHANGELOG.md by sentrivana in #5685

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[sentrivana]

👍🏻

[cursor]

Cursor Bugbot has reviewed your changes and found 2 potential issues.

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[sentrivana]

Looking great! Maybe add a comment on what _guaranteed_streaming_state means exactly?