First off, no, Google does not use scores from third party SEO tools or services. It doesn’t matter whether it’s about a website’s authority or a rating about spamminess, Google doesn’t use these scores at all.
Taking a step back, while some of these scores will be useless, that doesn’t mean all of them are. Transparently calculated scores can be useful to estimate your website’s standing or to point out actual issues.
They could help with the next steps, or perhaps even qualify the work that was done. Knowing how to score comes to be is critical in determining whether it makes sense for you. Let’s look at an example from Google. Chrome’s Lighthouse tool also creates scores.
Google doesn’t use these scores for search either. However, the score is transparently created based on various tests, which you can look at. With the overall score, you can estimate how well your website performs for those tests.
This can help you to spot issues, like maybe anchor text, that’s too short for usability, and those issues might be noticed by users or search engines. So once again, Google does not use scores from third party SEO tools for search. However, that doesn’t mean that they’re all useless. I hope this helps.