ci: Stop inheriting secrets in tests

[alexander-alderman-webb]

Description

Looks like the secrets are not needed.

Issues

Work towards #6718
Work towards PY-2573

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-2573

[github-actions]

Codecov Results 📊

✅ 90018 passed | ⏭️ 6298 skipped | Total: 96316 | Pass Rate: 93.46% | Execution Time: 313m 58s

📊 Comparison with Base Branch

Metric	Change
Total Tests	—
Passed Tests	—
Failed Tests	—
Skipped Tests	—

✨ No test changes detected

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2437 uncovered lines.
✅ Project coverage is 89.77%. Comparing base (base) to head (head).

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    89.77%    89.77%        —%
==========================================
  Files          192       192         —
  Lines        23819     23819         —
  Branches      8222      8222         —
==========================================
+ Hits         21382     21382         —
- Misses        2437      2437         —
- Partials      1347      1348        +1

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