[FEATURE] Migrate `next lint` to ESLint CLI

### Why do we need this improvement?

We need this because the `next lint` command is officially deprecated and scheduled for removal in Next.js 16. Currently, running `npm run lint` outputs the following warning:

"next lint is deprecated and will be removed in Next.js 16. For existing projects, migrate to the ESLint CLI."

If we do not address this now, our CI/CD pipelines and local linting scripts will break when we eventually upgrade to Next.js 16.

### How will this change help?

This change will:

- Future-proof the repository: It ensures smooth compatibility with future Next.js versions (v16+).

- Clean up build logs: It removes the noisy deprecation warnings from our CI checks and local development terminals.

- Standardize Tooling: Migrating to the native ESLint CLI aligns the project with standard ecosystem practices, decoupling the linter from the Next.js specific wrapper.

### Screenshots

_No response_

### How could it be implemented/designed?

We can implement this using the official Next.js codemod. The plan is:

- Run the automated migration tool:
```bash
npx @next/codemod@canary next-lint-to-eslint-cli
```
- Update `package.json`: Ensure the lint script is updated from `next lint` to `eslint`.

- Verification: Run `npm run lint` to confirm that the output is clean and rules are still being applied correctly.

### 🚧 Breaking changes

Yes

### 👀 Have you checked for similar open issues?

- [x] I checked and didn't find a similar issue

### 🏢 Have you read the Contributing Guidelines?

- [x] I have read the [Contributing Guidelines](https://github.com/asyncapi/.github/blob/master/CONTRIBUTING.md)

### Are you willing to work on this issue?

Yes I am willing to submit a PR!

Start with package.json and inspect the current lint script, then run the documented next-lint-to-eslint-cli codemod. Run npm run lint afterward and confirm that the deprecation warning is gone while the existing lint rules still apply.

Written by the indexing model from the issue text.