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>

.claude/skills/worktree-update/SKILL.md

@@ -88,6 +88,18 @@ continue to the next branch. The user must resolve before proceeding.
 After all merges, show the final state with `git log --oneline -N` (where N
 covers the new commits).
 
+#### Backup the shared database
+
+After successful merges on main, snapshot the database for git tracking:
+
+```bash
+make db-backup
+```
+
+This copies the shared `settledreach.db` (in the parent directory) to
+`docs/backups/settledreach.db.backup`. Stage and commit it with the merge
+if the file changed.
+
 ### 2b. Not on `main` — merge main into current branch
 
 ```bash