Add Biome + Ultracite example

[sgalanb]

Goals

• Create a new example based on Basic but replacing ESLint and Prettier with Biome.
• Include minimal per-package config files with modern rules using Ultracite presets.
• Include a .code-workspace file to fully support Biome's official VS Code extension.

Non-goals

No response

Background

The current Biome example doesn't work well with the official VS Code extension, because it's missing the .code-workspace file so it ignores the config files on each app/package and defaults to the root config instead. It also uses prettier for formatting, which is redundant because Biome has its own formatter that is very similar and it's built in.

Proposal

I use this setup every time I start a new project so I'm happy to put together the PR if you think it would be a good addition to the example list.