WebClient: Update frontend project to Vite

The web-client folder inside of this repository implements a Next project for all the tutorials. We should update this project to be based on the new Miden Vite project template.

Examine the existing web-client folder structure and the new Miden Vite project template. Compare configuration files (package.json, vite.config.js, etc.) and entry points. The goal is to migrate the Next.js setup to Vite while preserving tutorial functionality. Start by running the current project to understand its behavior, then replicate it using the Vite template.

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