CI: Add Biome Linting, Formatting, and Husky Pre-commit Hooks

This issue proposes migrating our code formatting and linting infrastructure from Prettier to Biome. Biome offers a unified toolchain for formatting, linting, and more, potentially simplifying our development setup and improving performance. This migration will involve updating our CI pipeline and pre-commit hooks (via husky).

https://biomejs.dev
https://typicode.github.io/husky/