fix: compile database package to JS for worker Docker stage

Worker was crashing with MODULE_NOT_FOUND for @codeboard/database
because the package only had TypeScript source and no build step.
Added tsconfig.json, changed build script to compile TS, and updated
Dockerfile to copy compiled dist into worker stage.

packages/database/package.json

@@ -2,13 +2,17 @@
   "name": "@codeboard/database",
   "version": "0.0.1",
   "private": true,
-  "main": "./src/client.ts",
-  "types": "./src/client.ts",
+  "main": "./dist/client.js",
+  "types": "./dist/client.d.ts",
   "exports": {
-    ".": "./src/client.ts"
+    ".": {
+      "import": "./dist/client.js",
+      "require": "./dist/client.js",
+      "types": "./dist/client.d.ts"
+    }
   },
   "scripts": {
-    "build": "echo 'database package uses prisma generate'",
+    "build": "prisma generate && tsc",
     "db:generate": "prisma generate",
     "db:push": "prisma db push",
     "db:migrate": "prisma migrate dev",

packages/database/tsconfig.json

@@ -0,0 +1,8 @@
+{
+  "extends": "../../tsconfig.json",
+  "compilerOptions": {
+    "outDir": "./dist",
+    "rootDir": "./src"
+  },
+  "include": ["src"]
+}