Add Biome for Formatting & Linting

Summary

Replace or consolidate existing formatting/linting tooling with Biome — a fast, single-binary formatter and linter for JavaScript/TypeScript. This covers the full monorepo: apps and packages.

Motivation

• Single tool replaces ESLint + Prettier with no config conflicts
• Significantly faster than the ESLint/Prettier combo (Rust-based)
• First-class Vite + React + TypeScript support out of the box
• One unified biome.json in the frontend
• Built-in import sorting (replaces eslint-plugin-import / prettier-plugin-sort-imports)

Acceptance Criteria

• biome.json added at frontend with agreed-upon rule set
• biome check runs clean against all packages
• biome check --write used for format-on-save (replace Prettier)
• CI step added: biome ci fails the build on violations
• Existing ESLint / Prettier configs removed (or scoped only to packages that can't migrate)
• package.json scripts updated: lint, format, check all delegate to Biome

Out of Scope

• Python files (handled separately by Ruff in the marketplace/ pixi projects)
• Biome does not process .toml, .md, or .yaml — existing tooling (or none) handles those

References

• https://biomejs.dev/guides/getting-started/
• https://biomejs.dev/guides/how-biome-works/#the-biome-json-file
• Migration guide from ESLint + Prettier: https://biomejs.dev/guides/migrate-eslint-prettier/