refactor: Restructure monorepo to apps/server/ and apps/web/ layout

Move src/ → apps/server/ and packages/web/ → apps/web/ to adopt
standard monorepo conventions (apps/ for runnable apps, packages/
for reusable libraries). Update all config files, shared package
imports, test fixtures, and documentation to reflect new paths.

Key fixes:
- Update workspace config to ["apps/*", "packages/*"]
- Update tsconfig.json rootDir/include for apps/server/
- Add apps/web/** to vitest exclude list
- Update drizzle.config.ts schema path
- Fix ensure-schema.ts migration path detection (3 levels up in dev,
  2 levels up in dist)
- Fix tests/integration/cli-server.test.ts import paths
- Update packages/shared imports to apps/server/ paths
- Update all docs/ files with new paths

docs/database.md

@@ -1,13 +1,13 @@
 # Database Module
 
-`src/db/` — SQLite database via better-sqlite3 + Drizzle ORM with hexagonal architecture.
+`apps/server/db/` — SQLite database via better-sqlite3 + Drizzle ORM with hexagonal architecture.
 
 ## Architecture
 
-- **Schema**: `src/db/schema.ts` — all tables, columns, relations
-- **Ports** (interfaces): `src/db/repositories/*.ts` — 10 repository interfaces
-- **Adapters** (implementations): `src/db/repositories/drizzle/*.ts` — 10 Drizzle adapters
-- **Barrel exports**: `src/db/index.ts` re-exports everything
+- **Schema**: `apps/server/db/schema.ts` — all tables, columns, relations
+- **Ports** (interfaces): `apps/server/db/repositories/*.ts` — 10 repository interfaces
+- **Adapters** (implementations): `apps/server/db/repositories/drizzle/*.ts` — 10 Drizzle adapters
+- **Barrel exports**: `apps/server/db/index.ts` re-exports everything
 
 All adapters use nanoid() for IDs, auto-manage timestamps, and use Drizzle's `.returning()` for atomic reads after writes.