chore(anthropic): Remove transaction-based tracing

[alexander-alderman-webb]

Description

Remove branches for the static trace lifecycle.
Also remove manual tracing API calls in tests, as the outer transaction is no longer needed.

Issues

Closes #7073

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 📊

✅ 88048 passed | ⏭️ 4056 skipped | Total: 92104 | Pass Rate: 95.6% | Execution Time: 285m 28s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📉 -45602
Passed Tests	📉 -42548
Failed Tests	—
Skipped Tests	📉 -3054

All tests are passing successfully.

✅ Patch coverage is 84.21%. Project has 2276 uncovered lines.
✅ Project coverage is 90.32%. Comparing base (base) to head (head).

Files with missing lines (1)

File	Patch %	Lines
sentry_sdk/integrations/anthropic.py	84.21%	⚠️ 3 Missing and 1 partials

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    90.24%    90.32%    +0.08%
==========================================
  Files          193       185        -8
  Lines        25724     23516     -2208
  Branches      9504      8626      -878
==========================================
+ Hits         23214     21240     -1974
- Misses        2510      2276      -234
- Partials      1435      1361       -74

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