I am looking for a way to require a specific work item type to be created whenever a new sprint is generated within Azure DevOps. The purpose behind this is to ensure that we can easily and properly pull metric information to show how many planned releases there are vs. unplanned (hotfix, emergency, etc.).
I originally attempted to setup a rule that whenever the iteration of a work item is changed, then there are additional fields that are required to be populated. However, this option is not available since you cannot create a rule based on the iteration path of a work item changing.
Obviously this is not directly associated to the above desired state, but it is our next option.
There isn't such a default feature in Azure DevOps that can meet your needs "require a specific work item type to be created whenever a new sprint is generated". If you want such a feature, you can submit a feature request on: https://developercommunity.visualstudio.com/report?space=21&entry=suggestion.
If you want to check how many iterations are there in the project, you can run this REST API Iterations - List. Then you can get the number of your iteration and you can see the timeFrame(past, current and future) of each iteration.