Laravel has a couple of tools to decorate your frontend. There is another theory of Frontend-Backend Separation, but I will make a comparison about Livewire, Inertia and Blade in this post.
A short introduction to Livewire, Inertia and Blade
Laravel is mainly a monolith favored framework, then the frontend backend coupling is one of the main ingredients of the framework. Laravel Blade is the built-in solution for many projects. However, you need more reactivity and it is the way beyond the capability of the Blade, you can choose the other. Blade is simply just a normal GET and POST thing. However, Livewire upgraded into the higher capability, single codebase and mainly fun. Inertia is an adapter between the Frontend JavaScript Frameworks and the backend, simply Laravel.
Pros and Cons
Each has its own pros and cons. Livewire has full potential for just easy modification of blade. In v4, it has a lot potential about upgrading the blade in single file component, lazy loading and load only when it needs, known as the island. Inertia has its potential about managing the state with the JS frameworks and send back to the backend.
When to choose and what to do?
If you are just a developer who is very proficient in working with PHP, a one man band, and a lazy developer who wants to add some features on your existing Laravel, choose Livewire. If you have great knowledge on JS or TS and you have some bird view of your application future, choose Inertia.
In other words, choose the total separation if you want to upscale a lot of things.