Eunice here from the Shopify Community, thanks for posting! That's a great question and I'd be happy to solve this mystery for you.
The good news is that you're completely on the right track. The homepage title and the homepage meta description under Online Store > Preferences does indeed show in Google search results for your store:
If you haven't already, I recommendsubmitting your sitemap to Google. All Shopify stores automatically generate a sitemap.xml file that contains links to all your products, product images, pages, collections, and blog posts. This is checked by Google once they notice it, and thereafter. However, Google does not check the site map each time it's crawled, therefore potential changes could be missed. Submitting your sitemap to Google will ensure changes are constantly being picked up.
I like the changes you've made by the way! The title looks a lot neater and the description gives you a good overview of what the site is about. When you make changes like this it can be beneficial to step in the shoes of your potential customers. When they see your store on their Google search results, will they be compelled enough to click?