Which password database system work with ansible?
Any system would do. You might need to write a wrapper. For example:

&gt; cat get-passwd-01.yml
- hosts: localhost
  gather_facts: no
  tasks:
    - command: ~/bin/get-passwd user9
      register: password
    - debug:
        msg: "passwd:{{ password.stdout }}"


.

&gt; ansible-playbook get-passwd-01.yml | grep msg
    "msg": "passwd: T4gpJtZ69R5cZD9zQh"