I'm trying to create new PersistentVolume manually and bind it to new PersistentValumeClaim, but once I create it, it does not create EBS volume.

As far as I understand you, you want to provision your storage manually, so you cannot expect that at the same time EBS volume, which is specific AWS storage type, will be created.

Look, what you defined in your yaml manifests is manual provisioning using your node local storage and has nothing to do with EBS. It seems to me that you confuse two concepts: manual and dynamic storage provisioning. Let's clarify it a bit. You could actually choose two different paths and decide to use either manual provisioning or dynamic one but not both of them at the same time.

1. as @Anton Kostenko suggested in his answer you may give up on using your local node storage, delete the mentioned fragment from your manifest and let Kubernetes and AWS with its EBS do it for you dynamically. You will need only to define PersistentVolumeClaim, choosing the proper storageClassName and PV will be provisioned automatically.

2. you may follow your original idea of creating PersistentVolume manually using hostPath. In this case you need to set storageClassName to manual in both PersistentVolume (which in this case is manually defined by you unlike in the 1st case) and PersistentVolumeClaim as in this example from official Kubernetes documentation. I've just checked it and it works perfectly. It's important to use same storage class so both PV and PVC can be bound together.

If you decide to choose the second path, your particular yaml manifests will look like that:

apiVersion: v1
kind: PersistentVolume
metadata:
  name: pv1
  labels:
    type: storage1
    app: rabbitmq1   
spec:
  claimRef:
    namespace: default
    name: pvc1
  accessModes:
  - ReadWriteMany
  capacity:
    storage: 1Gi
  hostPath:
    path: "/etc/rabbitmq"
  storageClassName: manual
---
apiVersion: v1
kind: PersistentVolumeClaim
metadata:
  labels:
    type: storage1
    app: rabbitmq1
  name: pvc1
spec:
  storageClassName: manual
  accessModes:
  - ReadWriteMany
  resources:
    requests:
      storage: 1Gi

Once you put it let's say in a file storage.yaml simply issue the following command:

kubectl apply -f storage.yaml

And in a while both your pv and pvc will be created and you should see their status as Bound:

$ kubectl get pv
NAME             CAPACITY   ACCESS MODES   RECLAIM POLICY   STATUS   CLAIM                   STORAGECLASS   REASON   AGE
pv1              1Gi        RWX            Retain           Bound    default/pvc1            manual                  33s


$ kubectl get pvc
NAME            STATUS   VOLUME           CAPACITY   ACCESS MODES   STORAGECLASS   AGE
pvc1            Bound    pv1              1Gi        RWX            manual         38s

You created a host path volume, that is from your spec:

  hostPath:
    path: "/etc/rabbitmq"

Just remove that path and K8s will create a new PV in with a EBS backend.