Setup `@jupyter/eslint-plugin`: both for extension code and for LSP on binder

### Problem

Some requirements related to creating Jupyter extensions are not picked up by the TypeScript type checker.

On Binder we already have LSP integration setup:

But it does not catch issues like incorrect plugin order:

Code

```ts
import {
JupyterFrontEnd,
JupyterFrontEndPlugin
} from '@jupyterlab/application';
import { ICompletionProviderManager } from '@jupyterlab/completer';
import { INotebookTracker } from '@jupyterlab/notebook';
const extension: JupyterFrontEndPlugin = {
id: 'completer',
autoStart: true,
requires: [ICompletionProviderManager, INotebookTracker],
activate: async (
app: JupyterFrontEnd,
notebooks: INotebookTracker,
completionManager: ICompletionProviderManager
) => {
console.log('JupyterLab custom completer extension is activated!');
}
};

export default extension;
```

### Proposed Solution

https://github.com/jupyterlab/eslint-plugin allows to spot these and saves time when developing extensions.

We should:
- integrate it with the extension codebase
- make sure it works on Binder
- but reconfigure require the rules which require plugin descriptions and command schema to be "info" rather than "error" as when prototyping these do not matter that much. Or maybe we should even have a toggle to disable these altogether? This could be a follow-up task

### Additional context