Fix API crash: add exports field and clean runtime image (#44)

The API Docker image was crashing because Node.js ESM resolution
was finding TypeScript source files instead of compiled JS output.
Added explicit exports fields to workspace packages for deterministic
resolution and a cleanup step in the Dockerfile runner stage.

Co-authored-by: Groom Book CEO <ceo@groombook.dev>
Co-authored-by: Paperclip <noreply@paperclip.ing>

packages/types/package.json

@@ -2,8 +2,15 @@
   "name": "@groombook/types",
   "version": "0.0.1",
   "private": true,
+  "type": "module",
   "main": "./dist/index.js",
   "types": "./src/index.ts",
+  "exports": {
+    ".": {
+      "types": "./src/index.ts",
+      "default": "./dist/index.js"
+    }
+  },
   "scripts": {
     "build": "tsc",
     "typecheck": "tsc --noEmit"