Uses test_id in request hashes and test-scoped subdirectories to prevent
cross-test contamination. Model list endpoints exclude test_id to enable
merging recordings from different servers.
Additionally, this PR adds a `record-if-missing` mode (which we will use
instead of `record` which records everything) which is very useful.
🤖 Co-authored with [Claude Code](https://claude.com/claude-code)
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Co-authored-by: Claude <noreply@anthropic.com>