I tried going down this road using Livewire Starter Kit + Filament v5. I could see that the directives were being applied (or at least it looked like they were) but I was able to actually render flux components- I was only getting text, no styling. I removed that snippet from the app service provider.
Instead I published a Filament custom theme. Then copy pasted the imports and source from app.css to the (filament) theme.css. I added the necessary "../../" to make them line up. I was then able to render flux ui.
I wasn't getting any errors in the console about missing files... but something wasn't perfect. Things like badges and buttons were coming in full width. i had to add 'w-fit' in the class attribute to make them look right. But things like <flux:heading level="2" size="xl">Heading</flux:heading> was working correctly.