Welcome to Shopify Community. My name is Olivia and I work here.
I'd be glad to help you out with this today. There's a few different reasons why you might be receiving some of Shopify's automatic emails, but not all.
Your inbox may have identified some of Shopify's sender addresses as 'spam'. Make sure to add both email@example.com and firstname.lastname@example.org to your inbox provider's "allow" or "safe sender" list.
This would be set-up in your Admin > General > Customer email section. If you are using a custom domain email address here, make sure to add Shopify's SPF record to your domain's TXT records. Doing so will prevent emails from being marked as spam when they are sent to your future customers. For more context, check out this similar thread I answered.
Make sure to cross these items off your checklist and you shouldn't run into this again.
Please let me know if you have other questions around this.