On a fresh install using Herd, Laravel 12 and the Livewire starting kit, everything is working perfectly fine after installing and building the production assets.
Did you reply "yes" upon installation when asked:
Would you like to run npm install and npm run build?
This part not only builds assets, but install all the packages first (npm install). If you said "no", then obviously you have to run it manually before building your assets.
You can also try to update you Laravel Installer and Herd, and try to create a brand new project to see if this makes any difference:
composer global update laravel/installer
For Herd, check for updates in the application.