Chore: Remove @eslint/compat and don't run all eslint rules in betterer (#97463)

* Remove eslint compat

* Remove fixup for testing library rules

* Make sure we don't ignore betterer eslint config from itself

* Update betterer to not run rules that are run in linting anyway

package.json

@@ -78,7 +78,6 @@
     "@betterer/eslint": "5.4.0",
     "@cypress/webpack-preprocessor": "6.0.2",
     "@emotion/eslint-plugin": "11.12.0",
-    "@eslint/compat": "^1.2.0",
     "@grafana/eslint-config": "8.0.0",
     "@grafana/eslint-plugin": "link:./packages/grafana-eslint-rules",
     "@grafana/plugin-e2e": "^1.11.0",