We are also having this issue, 2 years later, I understand that its good to get a reminder but can't it be worded 'order/subscription renewal' rather than 'new order'.
We are using our store for subscription to a digital product, which we send out on the new order and don't have to the following months.
The team are just seeing 'new order' and think they have to send another product out.
How do I contact Squarespace to make a feature request?