Hi Hayley, I've done SEO and digital marketing for over 15 years. I've not run into any SEO issues with Squarespace (it could use more customization, but out of the box, you absolutely can be successful in organic search). I used to have several websites on WP and moved them to Squarespace primarily because of ease of use issues (it's slow and clunky to work in WP) and because of page performance, speed and Core Web Vitals issues (all pages on my SS sites pass CWV with flying colors).
A quick site search shows that Google has indexed 10 of your blog posts (assuming it's under the /journal subdirectory). You can check this for your entire site or any subsection of your site by going into Google and typing site:https://www.kind-living.com or site:https://www.kind-living.com/journal for specifically your blog. Your XML sitemap contains the blog articles and they are not blocked in robots.txt.
Your domain looks brand new, so as others have said, it's going to take some time to build up any kind of organic search equity.
Yes you can use Google Search Console (GSC) to check your indexation report. If it's saying the pages have been discovered, but not indexed, it's more of a quality/trust/uniqueness issue.
You can help Google and other search engines better understand your business by giving more context to some of your pages. For example, I don't really see what locale you operate in without going to your Events page. Try to put more info in your footer and in your Contact Us page with country (and business name, address, phone if possible).
