Since Search Console says it has not been crawled, I would separate indexing from SEO rankings first. Backlinks help later, but Google has to be able to discover and understand the pages before they matter.
Check the exact product and category URLs in Search Console's URL Inspection tool. If they say discovered but not crawled, submit your XML sitemap and request indexing for a few important URLs. If they say excluded, look for noindex, redirects, duplicate canonical URLs, or pages blocked by robots.txt. It is worth testing one page type at a time: homepage, category, product.
For Square Online stores, the biggest practical SEO lift is often making category and product pages answer real buyer searches. Use page titles and opening copy that say what the item is, who it is for, material or specs, compatibility, size, delivery area, and any buying constraints. Product descriptions can be SEO friendly but still too generic if they do not match the terms buyers use.
I would also add internal links from the homepage and top categories to your priority products, then watch Search Console's Pages and Queries reports for impressions. No impressions usually means indexing or crawl issue; impressions with no clicks means title, meta, and offer clarity need work.
