Ansible connection role error while provisioning server TASK [connection : Warn about change in host keys]

You can run the test task that populates the connection_status variable (which apparently has an unexpected value) manually:

- hosts: <production_or_staging_host_defined_in_ansible>
  gather_facts: no
  tasks:
    - name: Check whether Ansible can connect as web
      command: |
        ansible <production_or_staging_host_defined_in_ansible> -m raw -a whoami -u web -vvvv
      delegate_to: localhost
      failed_when: false
      changed_when: false
      check_mode: no

(Minimal test ansible task taken from a tangentially related issue)

Put that YAML into a file in the Trellis project directory (e.g. test-connection.yml), replace <production_or_staging_host_defined_in_ansible> with the target system host name (as defined in ansible) and then run it manually:

ansible-playbook test-connection.yml -e env=<environment>

You can also run ansible in very verbose -vvvv mode in order to see what values stdout will have from that task. Does stdout have a string as value? You can post it here for further evaluation.