Ansible: Run tasks on specific hosts with var/fact from another host

Question

I'm trying to get the output from a command on the first host in group managers and execute it on the other hosts in the same group.

hosts file

[managers]
k8s01
k8s02
k8s03

[workers]
worker1
worker2
...

main.yaml

- name: Create token to join cluster
  shell: kubeadm token create --print-join-command
  run_once: true
  changed_when: false
  when: inventory_hostname == groups['managers'][0]
  register: kubernetes_join_command_result

-name: Set join command for managers
- set_fact:
    kubernetes_join_command_controlplane: "{{ kubernetes_join_command_result.stdout }} --control-plane"
  when: kubernetes_join_command_result.stdout is defined
  delegate_to: "{{ item }}"
  delegate_facts: true
  with_items: "{{ groups['managers'] }}"   


- name: Debug var
  debug:
    msg: 'Join Command: {{ kubernetes_join_command_result.stdout }}'

- name: Join managers into cluster      
  shell: "{{ kubernetes_join_command_controlplane.stdout }}"
  args:
    warn: no
  when: inventory_hostname != groups['managers'][0] and inventory_hostname in groups['managers']

Instead of running the join command in hosts k8s02 and k8s03, I get the output below.

TASK [managers: Join managers into cluster] ********************
skipping: [k8s01] => {"changed": false, "skip_reason": "Conditional result was False"}
TASK [manager: another task] ***************************

Answer 1

I believe your hosts is set to k8s01 or other group not containing k8s02 and k8s03.
That's why they are not run.

You shall add with_items: "{{ groups['managers'] }}" and delegate as you done in the second task -name: Set join command for managers.

- name: Join managers into cluster      
  shell: "{{ kubernetes_join_command_controlplane.stdout }}"
  args:
    warn: no
  when: inventory_hostname != groups['managers'][0] and inventory_hostname in groups['managers']
  delegate_to: "{{ item }}"
  delegate_facts: true
  with_items: "{{ groups['managers'] }}" 

Alternatively, depending on your design and scope. Do as answer from Botka and set the hosts as:
hosts: all
or
hosts: managers

Answer 2

The condition works as expected. For example, the inventory and the playbook below

shell> cat hosts
[managers]
k8s01
k8s02
k8s03

[workers]
worker1
worker2

shell> cat playbook.yml 
- hosts: all
  gather_facts: false
  tasks:
    - debug:
        var: inventory_hostname
      when:
        - inventory_hostname != groups.managers.0
        - inventory_hostname in groups.managers

give

shell> ansible-playbook -i hosts playbook.yml 

PLAY [all] ****

TASK [debug] ****
skipping: [worker1]
ok: [k8s02] => {
    "inventory_hostname": "k8s02"
}
skipping: [k8s01]
skipping: [worker2]
ok: [k8s03] => {
    "inventory_hostname": "k8s03"
}