Hi Violka,
Shopify has a great page explaining the workings of different attribution models and comparing how different services are using them. For example Google Ads has an attribution window of 30 days and it always attribute to last non-direct interaction in that window (and so does Google Analytics, citing: “it will give credit to the last touchpoint in a conversion journey unless it was a direct visit to your site. In that case, it will give credit to the last non-direct touchpoint.” ). Shopify on the other hand attributes, as you correctly said, to “direct” if that was the source of the session where the conversion took place. Here is the resource: https://www.shopify.com/blog/marketing-attribution.
We at Dhatma implemented our own web tracking and combining data from our tracker and what Shopify offers through API’s we are trying to give a greatly enhanced visibility to all this.
Happy selling!