[compiler] Remove playground postinstall script

The ci step for the playground already installs playwright browsers so
this step was unnecessary. It also doesn't work internally for our sync
scripts

ghstack-source-id: d6e761563759739cfdab0b65f55222f9a9346e8a
Pull Request resolved: #29841

compiler/apps/playground/package.json

@@ -8,7 +8,6 @@
     "vercel-build": "yarn workspaces run build",
     "start": "next start",
     "lint": "next lint",
-    "postinstall": "yarn playwright install",
     "test": "playwright test"
   },
   "dependencies": {