Re-enable running our eslint rules using ts-node (#159495)

Resubmission of #157532 with the following changes:

- Use `eslint-plugin-local` instead of `yarn` link to run our plugins
- Move our plugins to a top level `.eslintplugin` dir (as required by `eslint-plugin-local`)
- Update all names to `local/`

.vscode/settings.json

@@ -41,11 +41,6 @@
 			}
 		}
 	],
-	"eslint.options": {
-		"rulePaths": [
-			"./build/lib/eslint"
-		]
-	},
 	"typescript.tsdk": "node_modules/typescript/lib",
 	"npm.exclude": "**/extensions/**",
 	"npm.packageManager": "yarn",