I am encountering the same issue when using the ESM-approach that's outlined in https://livewire.laravel.com/docs/installation#manually-bundling-livewire-and-alpine.
Instead, I listen to the alpine:init event, and then just use the Alpine instance Livewire created.
Make sure you do not import Alpine from 'alpinejs' yourself, and of course also don't Alpine.start() yourself.
document.addEventListener('alpine:init', () => {
Alpine.plugin(Clipboard)
Alpine.data('myComponent', () => {
return {
...
}
})
});