feat: add unified check command and root-level formatting check

[surhomin]

This PR addresses two feature requests:

1. Adds a unified root-level check script that runs lint, typecheck, test, and formatting checks in sequence (closes Feature Request: Add unified repository validation script #305).
2. Updates root-level format and format:check to run Biome directly on the root folder. This ensures that formatting is checked at the repository root level (including config files) rather than just inside workspaces (closes Feature Request: Add root-level format:check workflow for repository consistency #316).

[cb-heimdall]

🟡 Heimdall Review Status

Requirement	Status	More Info
Reviews	🟡 0/1	Denominator calculation Show calculation 1 if user is bot 0 1 if user is external 0 2 if repo is sensitive 0 From .codeflow.yml 1 Additional review requirements Show calculation Max 0 0 From CODEOWNERS 0 Global minimum 0 Max 1 1 1 if commit is unverified 1 Sum 2