Use current babel/eslint integration

Fixes these `npm install` warnings:

> deprecated babel-eslint@10.1.0: babel-eslint is now @babel/eslint-parser. This package will no longer receive updates.
> deprecated eslint-loader@4.0.2: This loader has been deprecated. Please use eslint-webpack-plugin

.eslintrc.json

@@ -5,7 +5,7 @@
         "es6": true
     },
     "extends": ["eslint:recommended", "standard", "standard-react"],
-    "parser": "babel-eslint",
+    "parser": "@babel/eslint-parser",
     "parserOptions": {
         "ecmaVersion": "7",
         "ecmaFeatures": {

package.json

@@ -13,9 +13,9 @@
   },
   "devDependencies": {
     "@babel/core": "^7.5.4",
+    "@babel/eslint-parser": "^7.13.14",
     "@babel/preset-env": "^7.5.4",
     "@babel/preset-react": "^7.0.0",
-    "babel-eslint": "^10.0.3",
     "babel-loader": "^8.0.6",
     "chrome-remote-interface": "^0.28.0",
     "compression-webpack-plugin": "^6.0.0",
@@ -24,7 +24,6 @@
     "eslint": "^7.10.0",
     "eslint-config-standard": "^14.1.1",
     "eslint-config-standard-react": "^9.2.0",
-    "eslint-loader": "^4.0.2",
     "eslint-plugin-flowtype": "^5.2.0",
     "eslint-plugin-import": "^2.22.1",
     "eslint-plugin-node": "^11.1.0",
@@ -32,6 +31,7 @@
     "eslint-plugin-react": "^7.21.2",
     "eslint-plugin-react-hooks": "^4.1.2",
     "eslint-plugin-standard": "^4.0.1",
+    "eslint-webpack-plugin": "^2.5.3",
     "htmlparser": "^1.7.7",
     "jed": "^1.1.1",
     "mini-css-extract-plugin": "^0.11.0",

webpack.config.js

@@ -6,6 +6,7 @@ const extract = require("mini-css-extract-plugin");
 const TerserJSPlugin = require('terser-webpack-plugin');
 const OptimizeCSSAssetsPlugin = require('optimize-css-assets-webpack-plugin');
 const CompressionPlugin = require("compression-webpack-plugin");
+const ESLintPlugin = require('eslint-webpack-plugin');
 const CockpitPoPlugin = require("./src/lib/cockpit-po-plugin");
 
 const webpack = require("webpack");
@@ -24,6 +25,7 @@ const copy_files = [
 const plugins = [
     new copy({ patterns: copy_files }),
     new extract({filename: "[name].css"}),
+    new ESLintPlugin({ extensions: ["js", "jsx"] }),
     new CockpitPoPlugin(),
 ];
 
@@ -73,12 +75,6 @@ module.exports = {
 
     module: {
         rules: [
-            {
-                enforce: 'pre',
-                exclude: /node_modules/,
-                loader: 'eslint-loader',
-                test: /\.(js|jsx)$/
-            },
             {
                 exclude: /node_modules/,
                 use: "babel-loader",