Thanks for the suggestions. I tried all of these steps, but unfortunately the issue still persists.
I checked Apple System Status, made sure there were no pending Terms and Conditions, updated my billing address and credit card details, and also tried again later.
I’m creating the child account directly from my Mac through System Settings → Family → Add Member → Create Child Account. I’ve also tried the same process on a second Mac, with exactly the same result.
After entering all the child’s details and clicking Next, it processes for a few seconds and then simply stays on the same screen. There is no error message, and the child account is not created.
Any other suggestions would be appreciated.