cat inventory.yml
all:
   children:
      group1:
        children:
           subgroup1:
              hosts:
                 172.16.228.133
                 172.16.228.135

cat deploy_ssh.yml
---
- hosts: subgroup1
  become: true
  become_user: "root"
  tasks:
     - authorized_key:
        user: root
        state: present
        manage_dir: yes
        key: "{{ lookup('file', '/home/user/.ssh/ans_id_rsa.pub')  }}"

sudo ansible-playbook -i inventory.yml deploy_ssh.yml --ask-become-pass --ask-pass -u user
[sudo] password for user:
SSH password:
SUDO password[defaults to SSH password]:

PLAY [case1] *******************************************************************************************************************************************************************************************************************************

TASK [Gathering Facts] *********************************************************************************************************************************************************************************************************************
ok: [172.16.228.133 172.16.228.135]

TASK [authorized_key] **********************************************************************************************************************************************************************************************************************
ok: [172.16.228.133 172.16.228.135]

PLAY RECAP *********************************************************************************************************************************************************************************************************************************
172.16.228.133 172.16.228.135 : ok=2    changed=0    unreachable=0    failed=0

ansible correctly wrote my pubkey on .133 but seems to ignore .135