This isn't explicity covered in the container apps document, however you can see here in this section of creating an environment where the first step suggests to register Microsoft.ContainerService resource provider.
Additionally, the Microsoft.ContainerService resource provider is required for several Azure services, including:
Azure Kubernetes Service (AKS): For managing and orchestrating containerized applications using Kubernetes.
Azure Red Hat OpenShift: For deploying and managing containerized applications using Red Hat OpenShift.
Azure Container Apps: For executing event-driven, serverless code.
Azure Container Instances: For running containers without managing the underlying infrastructure.
Azure Service Fabric: For building, deploying, and managing scalable and reliable microservices using containers.
Solution: For your scenario. Yes, you could ask the owner or a contributor to register this service from the subscriptions->resource providers and then try creating a container app in the RG where you have permissions to create a resource.
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