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

package.json

@@ -4,6 +4,7 @@
   "description": "Multi-agent workspace for orchestrating multiple Claude Code agents",
   "type": "module",
   "workspaces": [
+    "apps/*",
     "packages/*"
   ],
   "main": "./dist/index.js",
@@ -12,12 +13,12 @@
   },
   "scripts": {
     "build": "tsc",
-    "dev": "tsx watch src/bin/cw.ts",
+    "dev": "tsx watch apps/server/bin/cw.ts",
     "clean": "rimraf dist",
     "test": "vitest run",
     "test:watch": "vitest",
     "test:coverage": "vitest run --coverage",
-    "dev:web": "npm run dev --workspace=packages/web"
+    "dev:web": "npm run dev --workspace=apps/web"
   },
   "keywords": [
     "claude",