Social Media Importance for SEO?

I'm a software dev with prior experience working on SEO for a large international company. I now own and operate a local service business. I don't use social media personally or professionally.

Do you have informed opinions on the importance of Social Media "integrations" on a website and how they correlate to SEO? On all SEO analysis tools I've seen there are checks for social media links and even, specifically, Google analytics.

My business website typically "scores" slightly above average for technical SEO and CWV - which is the primary goal. But is intentionally lacking social media links and Google analytics. Cookieless analytics are used, via Goatcounter (not a plug necessarily but I discovered the service from a HN post and am very happy with it!).

I understand SEO is somewhat opaque and there are many factors contributing to rankings etc. I would like to avoid social media links and hardcore tracking analytics but am always reminded these are missing when running SEO analysis tools.

Just throwing it out there to get some opinions and thoughts. My current thinking is it's not a big deal either way, especially for a local service business where word-of-mouth is a more powerful driver of traffic. I would like the business and website to earn higher search engine rankings but am also wary of integrating social media, tracking, etc.

Thanks for any input