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fix(responses): preserve replay state and prompt cache lineage #4879

Job	Run time
DSH Profile Packaging (windows-latest)	47s
Rust Build Check (macos-15)	18m 40s
Rust Build Check (windows-latest)	24m 9s
Shell Deploy Scripts	14s
CLI Tests (macos-15)	5m 3s
CLI Tests (ubuntu-latest)	6m 39s
Rust Build Check (ubuntu-latest)	9m 12s
Frontend Build	6m 18s
	1h 11m 2s