As part of running a playbook I’m setting up an agent and add a key to it:

- name: Start ssh agent
  hosts: localhost
  gather_facts: no
  vars_files:
    - common_vars.yml
  tasks:
    - name: Start the SSH agent
      shell: |
        ssh-agent -s
      register: ssh_agent_result

    - name: Extract the SSH Agent PID
      set_fact:
        ssh_agent_socket: "{{ ssh_agent_result.stdout | regex_search('(/tmp/ssh-[^;]+/agent.[0-9]+)') }}"

    - name: Add the SSH private key to the agent (using the SSH Agent PID)
      shell: ssh-add /home/max/projects/kw-infra-simplified/terraform/do-compose-private-instance-key.pem
      environment:
        SSH_AUTH_SOCK: "{{ ssh_agent_socket }}"

And then I use this SSH_AUTH_SOCK in the next play:

- name: Ping instances
  hosts: apps
  gather_facts: no
  vars:
    ssh_agent_pid: "{{ hostvars['localhost'].ssh_agent_pid }}"
    ssh_agent_socket: "{{ hostvars['localhost'].ssh_agent_socket }}"
    ansible_ssh_user: ubuntu
  environment:
    SSH_AUTH_SOCK: "{{ ssh_agent_socket }}"
  tasks:
    - name: Debug the extracted SSH Agent PID
      debug:
        msg: "SSH_AUTH_SOCK is {{ ssh_agent_socket }}"

    - name: Ping the apps instances
      ping:

Which works just fine and outputs the debug message "SSH_AUTH_SOCK is {{ ssh_agent_socket }}" with the correct path to the ssh-agent socket. However, it can’t connect to the remote host and when inspecting the output from the ssh:

ansible-playbook -vvvvv ping.yaml

I can see that the ssh doesn’t attempt to use the agent. What could be the reason for this? Is what I’m trying to do is even possible?