Automation Rule to set ship by date as X working days after order placed

We are facing the same issue more or less. Today we had a few orders that were picked and packed Friday night and Saturday morning. We did print labels for them and we have the email notification setting for our store to send emails to customers and notify the WooCommerce store at 3:30 pm on shipping day. This is the usual time when couriers pick up packages from us. However, the email notification was sent today (Saturday) and WooCommerce was notified, however, since it is a Saturday, no pick up actually took place and we still have the packages.
I tried to create 3 tags for orders that are placed on Friday evening, Saturday and Sunday and then I created 3 corresponding automation rules similar to what you mentioned @SpencerW . In other words Set the Ship Date after 2 days from the order date if there is a tag "Saturday order". However, the ship date is not changing. I also tried to reprocess automation rules thinking that the problem might be that the order was already imported. But even then, so adding the tag, reprocessing automation rules, also did not change the shipment date from today (Saturday).
Also another problem is that on Monday we will have 3 end of day reports (manifests) for our courier, one from each day during the weekend instead of one for all orders received over the weekend and the orders received on Monday.
I hope there is another way to do this automatically since changing the shipping date manually for each order received over the weekend is time consuming. Especially that weekends are busier than weekdays.

Yes would love for this to be added! Need to add ship date automatically but right now it includes Saturdays and Sundays as work days, which we do not work on.