Implement `@fastify/vue` using `vue-router/vite`

### Prerequisites

- [x] I have written a descriptive issue title
- [x] I have searched existing issues to ensure the feature has not already been requested

### 🚀 Feature Proposal

Instead of a custom path based routing implementation, implement `@fastify/vue` using the now core `vue-router/vite` plugin.

### Motivation

This will make path based routing behave the same as the now core vue-router vite plugin instead of a custom implementation, making it more expected, and giving it all the features of that more complete implementation.

### Example

_No response_