No, Facebook group doesn't have anything to work with or improve SEO for your website. It is just a channel to promote your services but as my experience then it is not effective because I promoted more on FB groups but no contacts or traffic from them.
Keep in mind that Facebook is just for marketing, not SEO.
I think social media isnt a direct Google ranking factor, but there's some correlation between the number of shares and a website's ranking. Social media is one of the best ways to promote content and be found online. Which is, ultimately, what SEO is all about. So, the Facebook groups that are somehow related to your niche can help you promote your services or products and, eventually, get more traffic.In my opinion, the higher traffic may lead to a better ranking. Here's an interesting article on this topic - https://searchenginewatch.com/2019/03/12/social-media-how-does-it-affect-seo/
While administering social media marketing through Facebook, you need to be utmost natural in delivering your messages and contents to the target audience. Increasing the frequency of people visiting your FB page can also help you in effectively enhancing your organic SEO performance.
In Google Analytics referrals from social media does counts, so in my opinion it has impact on ranking in SERPs. Google recognizes shares and links from social media, it's one of many factors influencing your position in SERP.