Hey - I'd suggest to use the cart in this case. This will allow you to add a note and pass to checkout! https://shopify.dev/api/storefront/unstable/mutations/cartNoteUpdate
I attempted to use the cart part of the Storefront API but I did not find a way to turn a cart into a Checkout without actually moving all the items from one instance to the other. There is no mutation to turn a cart into a checkout so I am using the checkout directly.
The checkout does not have a notes property/mutation to add so I will need to add the note to the order, which I am not being able to create given that I have another open ticket about that here:
Any movement on this? I am also unable to add a note and I also don't see using the cart api as an option as this was implemented after I started my project and there is no way of converting a cart into a checkout, meaning the developer is responsible for maintaining both copies and keeping them in sync which would be a nightmare.
I got this working by using the new