At the moment, there's no way to pass the pre-order button/status from one Shopify brand to another, as it's often powered by a custom theme or a 3rd party app. Any sort of customizations or 3rd party apps falls out of the scope of what Carro can sync between one store and another.
Currently, the only workaround is if the supplier marks the product as "Continue selling when out of stock" and the retailer includes that it's a pre-order in the product's title and or description. However, this can be confusing for customers, and most retailers opt to not sell pre-ordered products.
The Carro team is looking at alternative solutions for supporting this in the future, hopefully in 2022.