chore: Remove update_current_span

[sentrivana]

Description

Getting rid of custom APIs.

update_current_span never worked with span streaming anyway.

Issues

Part of https://linear.app/getsentry/issue/PY-2623/drop-custom-apis
Part of #6894

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

[linear-code]

PY-2623

[github-actions]

Codecov Results 📊

✅ 110580 passed | ⏭️ 5428 skipped | Total: 116008 | Pass Rate: 95.32% | Execution Time: 381m 51s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +10607
Passed Tests	📈 +11658
Failed Tests	—
Skipped Tests	📉 -1051

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2256 uncovered lines.
✅ Project coverage is 90.56%. Comparing base (base) to head (head).

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    90.25%    90.56%    +0.31%
==========================================
  Files          193       185        -8
  Lines        25441     23892     -1549
  Branches      9352      8798      -554
==========================================
+ Hits         22960     21636     -1324
- Misses        2481      2256      -225
- Partials      1436      1373       -63

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