chore: Replace deprecated gen_ai.system with gen_ai.provider.name

[alexander-alderman-webb]

Description

See the deprecation in sentry-conventions:

https://github.com/getsentry/sentry-conventions/blob/4311c7eda54367489251df327008fffedee5001d/model/attributes/gen_ai/gen_ai__system.json

Issues

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 📊

✅ 67586 passed | ⏭️ 3304 skipped | Total: 70890 | Pass Rate: 95.34% | Execution Time: 209m 15s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📉 -68076
Passed Tests	📉 -64249
Failed Tests	—
Skipped Tests	📉 -3827

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2713 uncovered lines.
❌ Project coverage is 87.86%. Comparing base (4c1fb64) to head (dc7fb8d).

Coverage diff

@@            Coverage Diff             @@
##        master       #PR       +/-##
==========================================
- Coverage    90.19%    87.86%    -2.33%
==========================================
  Files          193       181       -12
  Lines        25790     22342     -3448
  Branches      9532      8120     -1412
==========================================
+ Hits         23258     19629     -3629
- Misses        2532      2713      +181
- Partials      1432      1239      -193

---

Generated by Codecov Action