feat(core): add mergeAdvanceAutoSync project setting

Schema for what the merger should do in other worktrees still checked out
on the integration branch when it advances the branch ref. Modes:
  off          — legacy (user pulls manually)
  ff-only      — fast-forward only when other worktree is clean
  stash-and-ff — Smart Pull pipeline (default)

Threads through DEFAULT_PROJECT_SETTINGS, PROJECT_SETTINGS_KEYS (auto via
Object.keys), the docs settings table, and parity + persistence tests.
Merger consumption lands in the follow-up engine change.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

docs/settings-reference.md

@@ -203,6 +203,7 @@ Defaults from `DEFAULT_PROJECT_SETTINGS`; key scope from `PROJECT_SETTINGS_KEYS`
 | `mergeStrategy` | `"direct" \| "pull-request"` | `"direct"` | Completion mode (local direct merge vs PR-first). |
 | `directMergeCommitStrategy` | `"auto" \| "always-squash" \| "always-rebase"` | `"always-squash"` | Direct-merge commit routing mode. `always-squash` (default) forces the legacy squash path. `auto` keeps the legacy squash path for branches with zero or one substantive commit, but switches multi-substantive direct merges to a history-preserving rebase-and-merge/cherry-pick path so commit boundaries, subjects, and `Fusion-Task-Id` trailers survive on `main`. `always-rebase` always preserves per-commit history. Only applies when `mergeStrategy="direct"`. |
 | `mergeIntegrationWorktree` | `"reuse-task-worktree" \| "cwd-main"` | `"reuse-task-worktree"` | Auto-merge integration-root mode for direct merges only. `reuse-task-worktree` runs the rebase/conflict/audit/finalize cascade inside the task worktree so project-root `HEAD` and dirty state stay untouched. `cwd-main` preserves the legacy project-root integration path as an escape hatch. When `worktrunk.enabled=true`, worktrunk-managed merge/worktree handling still takes precedence and this setting is effectively advisory until the native path is used. |
+| `mergeAdvanceAutoSync` | `"off" \| "ff-only" \| "stash-and-ff"` | `"stash-and-ff"` | After the merger advances the integration-branch ref, what to do in **other** worktrees still on that branch (typically your project-root checkout). `off` leaves them alone; users must `git pull` or click the Merge Advance Notice banner's Pull button to bring their checkout forward — this is the surprise behavior that made `git status` look like the merge had been reverted. `ff-only` auto-fast-forwards only when the other worktree's index and working tree are clean; dirty worktrees stay untouched and the banner still surfaces for manual pull. `stash-and-ff` (default) runs the Smart Pull pipeline (stash → fast-forward → pop) so local edits survive across the auto-sync. Pop conflicts emit `merge:auto-sync` audit events with `outcome: "stash-pop-conflict"` and surface through the dashboard's existing stash-conflict modal. Only applies to direct merges. |
 | `integrationBranch` | `string` | `undefined` | Optional canonical project integration branch override. Resolution order for merge/self-healing/branch-conflict defaults is `integrationBranch` → legacy `baseBranch` → `origin/HEAD` symbolic ref → fallback `"main"`. This resolved value is used as `projectDefaultBranch` for `resolveTaskMergeTarget(...)`; task-level overrides still come from task metadata. |
 | `prerebaseAutoEnabled` | `boolean` | `true` | Master switch for pre-merge auto-prerebase policy. When enabled, merger checks divergence from `<task.baseCommitSha>` to local `main` and may rebase before Stage 1/2 rebases. Ignored when `worktrunk.enabled=true` (worktrunk-managed path defers this layer). |
 | `prerebaseHotFiles` | `string[]` | `[`"AGENTS.md"`, `"packages/core/src/store.ts"`, `"packages/core/src/db.ts"`, `"packages/engine/src/executor.ts"`, `"packages/engine/src/scheduler.ts"`, `"packages/engine/src/merger.ts"`, `"packages/dashboard/app/styles.css"`]` | Exact-path trigger list for auto-prerebase. If any listed file appears in `<task.baseCommitSha>..localMainHead`, merger runs prerebase first, then continues through the existing Stage 1/2 cascade. Empty array disables hot-file triggering. |