Ok, I solved it. The services in the docker-compose of Localstack MUST include cloudformation, completely missed that.
Adding cloudformation at the end of the SERVICES variable, the creation of the stack was successful.
localstack:
image: localstack/localstack-full
ports:
- "4566:4566"
- "${PORT_WEB_UI-8080}:${PORT_WEB_UI-8080}"
environment:
- SERVICES=s3,lambda,sts,secretsmanager,iam,cloudwatch,sns,cloudformation