fix(integrations): add the system prompt to the gen_ai.request.messages attribute

[constantinius]

Issues

Closes https://linear.app/getsentry/issue/TET-1453/py-anthropic-request-messages-format

[linear]

TET-1453 Py Anthropic - request messages format

[codecov]

Codecov Report

❌ Patch coverage is 76.92308% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.99%. Comparing base (027aa6e) to head (ad5ad47).
⚠️ Report is 7 commits behind head on master.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
sentry_sdk/integrations/anthropic.py	76.92%	0 Missing and 3 partials ⚠️

Additional details and impacted files

@@ Coverage Diff @@## master #5161 +/- ## ========================================== - Coverage 83.95% 82.99% -0.96%  ========================================== Files 180 181 +1 Lines 18226 18335 +109 Branches 3233 3259 +26 ========================================== - Hits 15302 15218 -84 - Misses 1934 2119 +185 - Partials 990 998 +8 

Files with missing lines	Coverage Δ
sentry_sdk/integrations/anthropic.py	81.97% <76.92%> (-0.30%)	⬇️

... and 16 files with indirect coverage changes