I want to start a docker compose with the cmd docker compose up inside a kubernetes pod

This is my deployment:

apiVersion: apps/v1
kind: Deployment
metadata:
  name: test-system
  labels:
    app: test
    name: test
spec:
  replicas: 1
  selector:
    matchLabels:
      app: test
  template:
    metadata:
      labels:
        app: test
    spec:  
      # init-container 
      initContainers:
      - name: init-docker-compose
        image: k8s-testsystem-init:origin-main-stable
        imagePullPolicy: Always
        securityContext:
          runAsUser: 0
          runAsGroup: 0
        command: ["/bin/sh", "-c"]
        args: ["cp -R /opt/docker /data && chmod -R 777 /data/docker && cat /tmp/.env >> /data/docker/.env"]
        volumeMounts:
          - name: compose-files
            mountPath: /data
          - name: docker-config
            mountPath: /tmp
      containers:
      # docker 
      - name: docker-test
        image: docker:latest
        command: ["/bin/sh", "-c"]
        args: ["cd /data/docker && docker commpose up"]
        securityContext:
           privileged: true
        ports:
        - containerPort: 80
        - containerPort: 443
        - containerPort: 5005
        - containerPort: 502
        volumeMounts:
          - name: compose-files
            mountPath: /data
      # volumes
      volumes:
        # modbus profiles volumes
        - name: compose-files
          emptyDir: {}
        - name: docker-config
          configMap: 
            name: docker-configmap
            items: 
              - key: env
                path: .env

If I create this resource the pod exits with:

Cannot connect to the Docker daemon at unix:///var/run/docker.sock. Is the docker daemon running?

If I remove the cmd and start it via shell everythin works fine.

How can I fix this?