Fix Docker build: compile TypeScript packages before runtime stage

The API Docker image was copying raw .ts source files for @groombook/db
and @groombook/types into the runtime stage, but tsx (the TS loader) is
a devDependency stripped by --prod install. Node.js cannot load .ts files
natively, causing ERR_UNKNOWN_FILE_EXTENSION at startup.

- Add build scripts to db and types packages
- Add outDir to types tsconfig
- Update package.json main fields to point to compiled dist/
- Build packages in dependency order in Dockerfile
- Copy only dist output to runtime stage

Co-Authored-By: Paperclip <noreply@paperclip.ing>

packages/db/package.json

@@ -2,9 +2,10 @@
   "name": "@groombook/db",
   "version": "0.0.1",
   "private": true,
-  "main": "./src/index.ts",
+  "main": "./dist/index.js",
   "types": "./src/index.ts",
   "scripts": {
+    "build": "tsc",
     "generate": "drizzle-kit generate",
     "migrate": "drizzle-kit migrate",
     "seed": "tsx src/seed.ts",

packages/types/package.json

@@ -2,9 +2,10 @@
   "name": "@groombook/types",
   "version": "0.0.1",
   "private": true,
-  "main": "./src/index.ts",
+  "main": "./dist/index.js",
   "types": "./src/index.ts",
   "scripts": {
+    "build": "tsc",
     "typecheck": "tsc --noEmit"
   },
   "devDependencies": {

packages/types/tsconfig.json

@@ -5,7 +5,8 @@
     "moduleResolution": "NodeNext",
     "strict": true,
     "noUncheckedIndexedAccess": true,
-    "skipLibCheck": true
+    "skipLibCheck": true,
+    "outDir": "./dist"
   },
   "include": ["src"]
 }