chore(tooling): upgrade TypeScript to 7 (#1581)

## Description

Upgrade the workspace compiler from TypeScript 6.0.3 to 7.0.2 independently of better-sqlite3 13. The upgrade exposed duplicate Drizzle type identities because the CLI directly uses the Better SQLite adapter without declaring Drizzle’s optional `@types/better-sqlite3` peer; adding the shared catalog dependency leaves one Drizzle resolution.

Tracks `codemem-jnd6.7.4`. Supersedes closed PR #1579.

## Type of Change

- [ ] 🚀 Feature (new functionality)
- [ ] 🐛 Bug fix (fixes an issue)
- [ ] 📚 Documentation (docs-only change)
- [x] 🔧 Maintenance (refactor, chore, CI, etc.)
- [ ] 🧪 Testing (test-only changes)

## Testing

- [x] Relevant checks pass locally (`pnpm run tsc`, `pnpm run lint`, `pnpm run test`)
- [ ] Added/updated tests for changes
- [x] Manually verified changes work as expected

Additional validation: TypeScript 7.0.2 version check; one Drizzle package resolution; full `pnpm run check` with 5,740 passing tests; full workspace build including Worker bundle dry-run; frozen lockfile installation; and independent code review.

## Checklist

- [x] Code follows project style (`pnpm run lint` passes for touched files)
- [x] Self-review completed
- [x] Documentation updated (not needed; no user-facing behavior changed)
- [x] No new warnings introduced