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