Hello, after trying many things to make this work, I will drop here the solution, thanks @Malthi Durga Reshma and @Akram Kathimi for your help:
1.- Once you deploy your AKS cluster, you need to get the Kubelete Managed Identity (Not the user managed identity for your bicep deployment).
2.- You need to assign the next roles to the Kubelet Identity:
- Contributor Role with scope: Application Gateway.
- Reader role with Scope: Application Gateway's Resource Group.
- Network Contributor with scopes: App Gateway's Subnet and your BackEnd Services Subnet.
- Managed Identity Operator with scope: User Managed Identity used for your Bicep Deployment.
I hope this is helpful for others in the future.