Feature Request: Add unified repository validation script

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

## Problem

The repository currently exposes separate validation commands such as:

- `yarn lint`
- `yarn typecheck`
- `yarn test`
- `yarn format:check`

However, there is no single unified validation command for contributors and CI workflows.

## Proposed Improvement

Add a root-level validation script such as:

```json
"check": "yarn lint && yarn typecheck && yarn test && yarn format:check"

### Describe the solution you'd like

Add a unified root-level validation script for contributor and CI workflows.

Example:

```json
"check": "yarn lint && yarn typecheck && yarn test && yarn format:check"

### Describe alternatives you've considered

_No response_

### Additional context

```md id="q6k4cw"
Contributors can currently run each validation command individually, but a unified workflow would improve consistency and onboarding.

Start with the root package manifest and inspect the existing yarn lint, typecheck, test, and format:check scripts. Add the unified check command so each validation step runs in sequence, then run it from the repository root. Done means the command is available for contributors and CI and completes successfully when all existing checks pass.

Written by the indexing model from the issue text.