You are absolutely correct, typo on my part in the second URL - apologies.
I tried to edit my answer but I can’t as it’s the accepted solution. For anyone in the future who wanders on here the corrected urls in my solution are:
GET
https://{StoreName}.myshopify.com/admin/api/2022-10/orders/{order_id}/fulfillment_orders.json
POST
https://{StoreName}.myshopify.com/admin/api/2022-07/fulfillments.json