Thank you @OliverIshmael. I've been able to resolve the issue.
For the Region and Site fields, your calculated expression needs to be changed to the following:
- return "1" for the Region field
- return "2" for the Site field
The reason for this is because the value above represents the code in the coded-value domain applied to those fields. When the form loads in Field Maps, you will see the correct descriptions of "North West Wales" and "Coed y Brenin Forest Park" applied and the contingent values will work successfully.
In arcade the syntax above assumes the value getting passed is the code and not the description, which is why it wasn't working previously.
Thanks
-Kevin