fix(integrations): atomically record generated skill files

[Gambit-Checkmate]

Summary

• route generated integration files through IntegrationManifest.record_file so writing and manifest tracking happen together
• add Claude integration coverage ensuring every generated SKILL.md, including speckit-converge, persists in claude.manifest.json

Fixes #4273

Validation

• python -m compileall -q completed for both modified Python files

The full repository test suite is not available in the local environment, so CI should run the integration test.

[mnriem]

The two modified files need to be normalized back to LF before this can be reviewed. The repository enforces * text=auto eol=lf, but this commit introduces mixed CRLF/LF endings across almost every line: the displayed diff is 2,778 additions and 2,772 deletions, while git diff -w reduces it to roughly 22 changed lines. This makes the substantive change effectively unreadable and creates unnecessary merge risk.

Please also demonstrate that the regression test fails on main before the implementation change. As written, it appears to assert behavior the existing write_file_and_record() path already provides, so it does not yet establish that switching from write-then-record_existing() to record_file() fixes the reported upgrade scenario.

Posted on behalf of @mnriem by GitHub Copilot (model: GPT-5.6 Sol).