We can add a message to a product while adding it to the cart as per this question here - Option and notes fields after cart at checkout for order, not just line items
But is there a way to add a message during the actual check out process, before the payment is submitted? At any stage during the checkout?
If we create a custom field in Commerce > Order Fields, can we add this to the checkout for the customer to fill out?
I think you're misreading that question - it too is asking about adding a message to a cart, not line items.
The second answer to the question you linked - https://craftcms.stackexchange.com/a/22777/340 - has what you need - it talks about notes on orders, rather than line items.
This can be done at any point in the order/checkout process - any call to update the cart that supplies a value for that field will result in the data being added.
Looks like the official Commerce docs have info on this here: https://craftcms.com/docs/commerce/3.x/update-cart-custom-fields.html
