This ask is dependent on the completion of T350226: [MSMF] Upgrade Laravel and peer dependencies

Laravel mix, a webpack based client-side asset build configuration system, has not seen updates in a few years. This is due to the fact that in newer versions of the Laravel stack, mix has been replaced with Vite as the system of choice, particularly because it is also the recommended build system for Vue.

In addition, while Migrating to Vue 3 it was noticed that mix is struggling with providing accurate typescript compilation error information regarding line numbers and additional errors.

In order to keep with the times, and ensure better support for Vue and Typescript, a migration to Vite in Mismatch Finder is needed.

Notes:

• Migration Guide from mix to Vite: https://github.com/laravel/vite-plugin/blob/main/UPGRADE.md#migrating-from-laravel-mix-to-vite

Acceptance Criteria:

• Laravel Mix is replaced by Vite in all client-side build operations.