Looking at the documentation, CDK construct for SNS Text Messaging doesn't exist nor do CloudFormation template for it.

CDKTF has it because, as far as I know, TF doesn't use CloudFormation but uses AWS API instead.

If you look at https://github.com/markilott/aws-cdk-configure-sns/blob/main/lib/sns-config-stack.ts#L108-L123, it's using AwsCustomResource. That's what you can do as well, create your own CustomResource.