Does Pulumi provide a arbitrary way to call a custom REST api to create custom resources which then can be managed or would this be a good use case to create a dynamic provider in my project?

Yes it does, you can inherit from CustomResource and pass something of your own that implements ResourceProvider (or ProviderResource, not sure of the name)

Dynamic Providers - check out azure-ts-dynamicprovider in the examples repo

Awesome thanks guys!