Simplify Template ESLint Configuration (#35529)

Summary:
Pull Request resolved: #35529

ESLint configuration is derived from `react-native/eslint-config`, which has supported Flow, vanilla JS, and TypeScript.

react-native-community/react-native-template-typescript#238 and a related PR ended up adding new rules to the TypeScript config, to fix bugs with TS linting. It required a followup change, to specify the parser/plugin, and explicity reference them as devDependencies. react-native-community/react-native-template-typescript#240

`react-native/eslint-config` already includes setting the plugin/parser. But overriding rules requires declaring that again, and directly referencing a plugin means a need for the app to declare dependencies, since ESLint resolves modules from the current config.

The rules overridedn were later fixed in `react-native/eslint-config`, which is really the right place for the fix (e.g. #32644). I noticed this when deriving from the TS template in #32644 and removed the rule overrides, but didn't have the historical context to realize this means we can then:
1. Remove the explicit parser/plugins since `react-native/eslint-config` already sets them, and we are no longer overriding any rules.
2. Remove the devDependencies, to let the versions be managed entirely by `react-native/eslint-config`.

Changelog:
[General][Changed] - Simplify Template ESLint Configuration

Reviewed By: cortinico

Differential Revision: D41652699

fbshipit-source-id: 8e3313dbf27407c5866f3c2432cffc2ecec1b01d

Author: NickGerleman

template/_eslintrc.js

@@ -1,6 +1,4 @@
 module.exports = {
   root: true,
   extends: '@react-native',
-  parser: '@typescript-eslint/parser',
-  plugins: ['@typescript-eslint'],
 };

template/package.json

@@ -22,8 +22,6 @@
     "@types/jest": "^29.2.1",
     "@types/react": "^18.0.24",
     "@types/react-test-renderer": "^18.0.0",
-    "@typescript-eslint/eslint-plugin": "^5.37.0",
-    "@typescript-eslint/parser": "^5.37.0",
     "babel-jest": "^29.2.1",
     "eslint": "^8.19.0",
     "jest": "^29.2.1",