Why ansible script sees different environment than SSH?

I created simple check.py script:

import getpass
import sys
import os

print(getpass.getuser())
print(sys.executable)
print(os.popen("which python3").read())
print(os.popen("cmake --version").read())

I use ansible the script inside of mac machine and read output. Ansible shows output:

administrator
/usr/local/bin/python3
/usr/bin/python3
/bin/sh: cmake: command not found

... but if I SSH to the machine with the same administrator account, the same script returns:

administrator
/usr/local/bin/python3
/usr/local/bin/python3 # different!
cmake version 3.25.2 # different!

Why is there a difference in os.popen output and how can I persuade ansible/python to return the same output as I see in the SSH?

Here are my ansible files:

ansible.cfg:

[defaults]
inventory = hosts
host_key_checking = False
action_warnings = False
deprecation_warnings = False

main.yml:

- name: Run a check script
  ansible.builtin.script: check.py
  args:
    executable: /usr/local/bin/python3
  register: output
- debug: var=output.stdout_lines

group_vars\all.yml:

ansible_user: administrator
ansible_password: admin_password
ansible_become:
ansible_become_user: root
ansible_become_pass: root_password
workdir: /Users/Shared/Jenkins
node_type: bare_metal
env: production

I used print(os.environ) line in python script to find out differences between ansible and ssh environment. Then I added environment setting to main.yml to synchronize paths:

- name: Run a check script
  ansible.builtin.script: check.py
  args:
    executable: /usr/local/bin/python3
  register: output
  environment:
    PATH: /usr/local/bin:{{ ansible_env.PATH }}:/Applications/CMake.app/Contents/bin
- debug: var=output.stdout_lines