test: Add streaming API tests

[sentrivana]

Description

Add streaming versions of tests in test_api.py

Issues

Part of #5395

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

[cursor]

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[github-actions]

Codecov Results 📊

✅ 96635 passed | ⏭️ 6340 skipped | Total: 102975 | Pass Rate: 93.84% | Execution Time: 348m 7s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +200
Passed Tests	📈 +200
Failed Tests	📉 -1
Skipped Tests	📈 +1

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2507 uncovered lines.
✅ Project coverage is 89.7%. Comparing base (base) to head (head).

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    89.69%    89.70%    +0.01%
==========================================
  Files          193       193         —
  Lines        24330     24330         —
  Branches      8578      8578         —
==========================================
+ Hits         21820     21823        +3
- Misses        2510      2507        -3
- Partials      1397      1396        -1

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