My name is Rae, and I work for Shopify. I'm happy to help out here.
To confirm, when you search for your store on Google, does the correct meta description show up? If your old description is still visible, this is due to the information not necessarily updating on Google right away once the meta description is updated on Shopify's end. However, finding and submitting your sitemap can help alert Google to re-index your site and update this information. While Google doesn't guarantee how long it will take to update this on their end, completing this process has been known to speed things up for other merchants, so it's a great step to take.
Additionally, based on the screenshot you shared, it looks like your meta description isn't updated when links to your store are shared on social media platforms, too. With this in mind, I recommend using Facebook's Sharing Debugger tool to refresh the website information shown on social media posts that contain links to your store. We have more details on how this works right here in our Help Center.
Please give these steps a try and keep me posted on how it goes!