web: vite + react + tailwind hello page with dark-mode toggle

Workspace packages export TS source under a 'source' condition used by
vite, node (--conditions=source) and tsc.

Task: M0-T4

apps/api/package.json

@@ -5,7 +5,7 @@
   "license": "AGPL-3.0-or-later",
   "type": "module",
   "scripts": {
-    "dev": "node --watch --env-file-if-exists=../../.env --conditions=development src/index.ts",
+    "dev": "node --watch --env-file-if-exists=../../.env --conditions=source src/index.ts",
     "build": "tsc -p tsconfig.build.json",
     "typecheck": "tsc --noEmit"
   },