custom checkout order form field API

Yes. See https://woocommerce.github.io/woocommerce-rest-api-docs/#order-properties -> “Order – Meta data properties”

Can’t help here with the specific implementation though as this is outside the realm of support we can provide.

If you believe there to be an error with the REST API, feel free to submit a GH issue. But if you need help with the customization you’re doing – you may need to hire/contract another developer for help.