Feature Request: Add root-level format:check workflow for repository consistency

### Is your feature request related to a problem? Please describe.

The repository currently exposes root-level workflows for linting, testing, and type checking, but does not provide a unified formatting validation command.

Adding a root-level `format:check` script would improve contributor workflow consistency and simplify formatting validation during CI and local development.

Example:

```json
"format:check": "pnpm biome check ."

Inspect the repository's root-level scripts and existing linting, testing, and type-checking workflows first. Add the requested format:check entry using the provided pnpm Biome command, then run it locally and confirm it validates repository formatting.

Written by the indexing model from the issue text.