After many attempts, I made it work using the customLivenessProbe parameter and specifying it in the values block like below.
I tried it before and it failed but I think that was due to a misconfiguration in the customReadinessProbe block.
Thanks to @Marko E for the help !

resource "helm_release" "rabbitmq" {

  count         = var.deploy_map.eema ? 1 : 0
  repository    = var.repository
  description   = var.description
  lint          = var.lint
  verify        = var.verify
  name = var.name
  version = var.version
  chart = var.chart
  namespace = var.namespace
  create_namespace = var.create_namespace
   
  set {
    name  = "service.type"
    value = var.service_type
  }

  set {
    name = "readinessProbe.enabled"
    value = false
  }

  values = [
    <<EOF
service:
  annotations:
    service.beta.kubernetes.io/azure-load-balancer-internal: "true"
    service.beta.kubernetes.io/azure-load-balancer-internal-subnet: "my-subnet"
customLivenessProbe: 
  exec:
    command:
      - bin/sh
      - '-ec'
      - rabbitmq-diagnostics -q ping
  initialDelaySeconds: 120
  timeoutSeconds: 20
  periodSeconds: 30
  successThreshold: 1
  failureThreshold: 6
EOF
  ]
}