feat(db): add database backup/restore tooling

- tooling/db-backup: copies shared settledreach.db to docs/backups/
  for git tracking (main branch only)
- tooling/db-install: restores from backup for new clones
- make db-backup / make db-install Makefile targets
- worktree-update skill runs make db-backup after merges on main

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

tooling/db-install

@@ -0,0 +1,25 @@
+#!/usr/bin/env bash
+# Restore the shared database from the git-tracked backup.
+# Use after cloning or when the shared database is missing.
+# Called via `make db-install`.
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"
+WORKTREE_ROOT="$(dirname "$SCRIPT_DIR")"
+DB_PATH="$(dirname "$WORKTREE_ROOT")/settledreach.db"
+BACKUP_PATH="$WORKTREE_ROOT/docs/backups/settledreach.db.backup"
+
+if [ -f "$DB_PATH" ]; then
+    echo "error: shared database already exists at $DB_PATH" >&2
+    echo "       delete it first if you want to restore from backup" >&2
+    exit 1
+fi
+
+if [ ! -f "$BACKUP_PATH" ]; then
+    echo "error: backup not found at $BACKUP_PATH" >&2
+    echo "       run 'make db-backup' on the main branch first" >&2
+    exit 1
+fi
+
+cp "$BACKUP_PATH" "$DB_PATH"
+echo "ok: restored $(du -h "$DB_PATH" | cut -f1) to $DB_PATH"