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gsxdsm 7b839069b5 FN-6420: run dependency sync in AI merge worktrees

Run configured or inferred dependency installs before AI merge verification uses the clean-room worktree.

- Add shared dependency-sync helpers with install marker caching for inferred lockfile installs.
- Run dependency sync during AI clean-room merges and audit/log the command, skip reason, and duration.
- Reuse the helper from merger paths while documenting the new behavior and covering install success/failure cases.

Files changed:
 .changeset/fn-6420-ai-merge-dependency-sync.md     |   5 +
 docs/architecture.md                               |   2 +-
 docs/settings-reference.md                         |   2 +-
 .../src/__tests__/executor-step-session.test.ts    |   5 +-
 .../merger-ai-dependency-install.slow.test.ts      | 269 +++++++++++++++++++++
 packages/engine/src/merge-dependency-sync.ts       | 144 +++++++++++
 packages/engine/src/merger-ai.ts                   |  31 +++
 packages/engine/src/merger.ts                      | 120 +++------
 packages/engine/src/run-audit.ts                   |   1 +
 9 files changed, 484 insertions(+), 95 deletions(-)

Fusion-Task-Id: FN-6420

Fusion-Task-Lineage: 49353cb6-4953-4670-b620-a90331f048dc

2026-06-13 21:09:12 -07:00