Are you asking how inertia interacts with Laravel to pass the serverside variable through the error bags to page props that are read by the vue components on the frontend in the browser?
I am interested in exact how this works too, if this is what you are asking.
Laravel already converts ValidationException to a proper validation error, and if the request is requesting json, it is converted to that. So Inertia simply builds on top of that
@anjanesh No it is always converted to json. If its a request from javascript (router.get etc) it returns is as plain json, and if its a full page reload, it gets injected in the <div id="app"> as inline json