Select Ads: Write. That is the only scope the ShopMy integration needs, and every other permission on the list can stay unchecked.
The integration writes your ShopMy ad spend into Triple Whale and does nothing else, so it has no reason to touch your orders, customers, products, or subscriptions.
If the scope is missing
ShopMy checks your key for Ads: Write when you save it. A key without that permission is rejected on the spot with clear error.
Matching your shop domain
The shop domain you enter on the ShopMy side has to match the domain on your Triple Whale account. If the two differ, the connection won't complete.
Related: [How do I connect ShopMy to Triple Whale?]