You are doing it correctly Stewart!
Instead of using the Book button, try creating the booking for the work order by adding it via the booking sub-grid on the work order form. I have added several additional mappings before and it has worked as expected. I typically add bookings via the sub-grid on the work order or by dragging and dropping on the schedule board so I wouldn't have noticed if the Book button did not honor the mappings. So I just test the Book button in the latest version of field service and as you have already noticed it does not honor the mappings, but it does if you use the sub-grid which makes sense since this is OOB behavior. Field Service has additional features like this across the product and in most cases it does honor the mapping relationships, so I would put in a support ticket MS and find out if this is intentional or a bug. In the meantime you can create a workflow or flow to back fill the data once the record is created.
Not sure you need to log a support ticket, you are probably looking at the wrong relationship.
Try looking at the mapping between your schedule entity and the Resource Requirement instead. I've written shortly about it at the end of this blogpost: https://saralagerquist.com/2019/01/14/get-started-with-universal-resource-scheduling/
Hope this helps!
What fields do you want to map? If you have to create new ones there might be things that have to be changed in the Scheduling Assistant filters so they are used in the query itself, but let me know what fields and I'll try to guide you.
This is the relationship you do it from (Work Order 1:N Resource Requirement):
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