While I'm no SEO expert, I did want to chime in on your question! When it comes to Google, they use both relative and authoritative results to determine what appears for the user. Ultimately, you can't have one without the other, so backlinking is a valuable tool in increasing your authoritative score with Googles' algorithm. I think what's more important here, is where you're paying to have your store backlinked as this will greatly impact the volume you receive from both the place that posted your store and your organic traffic.
Paying a newspaper to backlink your store would be useful given the traffic, but if the audience the paper targets doesn't align with your target audience, then this wouldn't prove to be a strong backlink. For this, I'd recommend looking into other ways you can backlink your store, such as writing reviews on the apps you use within the Shopify app store. You could also reach out to popular bloggers that attract your target audience as this can also help with driving both paid and organic traffic as this would be a stronger backlink then a newspaper can provide. I also found a blog post from Referral Candy that dives into backlinks a little further should you need it!
Let me know what you think!
Backlinks, when created from "backlink farms" or backlink lists, such as the list of stores a person visits, due to being acquired at no cost, carry no volume for Google. However, backlinks still matter [they do on a much smaller scale now, and predictions are they won't matter virtually anything within the next 5 years], they still matter, if they're being done the correct way. Now this is a much more complicated topic on how to do the backlinks the right way, but yes - they still DO matter!