Filament as an admin panel would essentially be "separate" to your site (unless you opt to make it part of the entire application as such and build upon it).
My blog for example utilises Filament for the "CMS" part of things and yes, where I've extended its functionality to do what I need for that, it has been written within the realms of Livewire (which in Filament tbh, is almost abstracted when you read the Filament docs on how to extend its core). The rest of the blog (ie: the public-facing site) currently only uses Laravel and blade... but I would have no hesitation in building my site/application with Inertia & Vue and using Filament as the admin panel... the 2 would be separate entities so to speak. Filament essentially just populates the database, the Laravel part of the application then retrieves that data and you can pipe that into whatever front end (or even an API if you wished) as you desire.. be that Inertia&Vue/React/Angular, etc.