Welcome to the Community, we are so happy to have you here with us.
This is great feedback! I talked to the product team who was working on this integration and have some information for you. When the team was working on adding gift notes to the integration, they also looked into adding the gift wrap fields you mention.
During their testing, they realized that this implementation was more complex than estimated and found they needed to research this further. Since they knew this would take time, they went ahead with the update to implement gift messages now so users would not need to wait, but they are still actively looking into the gift wrap fields.
While we don't have an ETA on this, I would strongly recommend keeping your eyes out for our ShipStation Improvements & Bug Fixes Blog series as this is where announcements like this are shared.
-Erin: Your Friendly ShipStation Community Manager
As of Friday, April 16th, 2021, you can now map the gift wrap + price to one of the 3 custom fields in ShipStation.
To do this, edit your Etsy store settings in ShipStation. Then select Gift wrap + Price from one of the three custom field drop downs and save your changes. Going forward, those details will import into the custom field you selected for your Etsy orders.