in on list vs string

$ cat /tmp/test.yml 
---
- hosts: localhost
  gather_facts: false

  vars:
    with_test: |-
      echo username cisco privilege 15 secret 5 \$1\$..
      echo username test privilege 15 secret 5 \$1\$..
    without_test: |-
      echo username cisco privilege 15 secret 5 \$1\$..
      echo username toto privilege 15 secret 5 \$1\$..

  vars_prompt:
    - name: test_user
      prompt: "test user (yes/no): "
      defaut: yes
      private: no

  tasks:
    - shell: "{{ test_user | bool | ternary(with_test, without_test) }}"
      register: username_contents
      changed_when: false

    - name: debug registered vars we will use
      debug:
        var: "{{ item }}"
      loop:
        - username_contents.stdout_lines
        - username_contents.stdout

    - name: Check that 'test' is in stdout_lines (wrong)
      debug:
        msg: Found 'test' in stdout_lines (but that's probably a lie)
      when: ('test') in username_contents.stdout_lines

    - name: Check that 'test' is not in stdout_line (wrong)
      debug:
        msg: Did not find 'test' in stdout_lines (but that's probably a lie)
      when: ('test') not in username_contents.stdout_lines

    - name: Check that 'test' is in output (good)
      debug:
        msg: Found 'test' in entire output
      when: ('test') in username_contents.stdout

    - name: Check that 'test' is not in output (good)
      debug:
        msg: Did not find 'test' in entire output
      when: ('test') not in username_contents.stdout
      
$ ansible-playbook /tmp/test.yml 
test user (yes/no): : yes

PLAY [localhost] **************************************************************************************************************************************************************************************************

TASK [shell] ******************************************************************************************************************************************************************************************************
ok: [localhost]

TASK [debug registered vars we will use] **************************************************************************************************************************************************************************
ok: [localhost] => (item=username_contents.stdout_lines) => {
    "ansible_loop_var": "item",
    "item": "username_contents.stdout_lines",
    "username_contents.stdout_lines": [
        "username cisco privilege 15 secret 5 $1$..",
        "username test privilege 15 secret 5 $1$.."
    ]
}
ok: [localhost] => (item=username_contents.stdout) => {
    "ansible_loop_var": "item",
    "item": "username_contents.stdout",
    "username_contents.stdout": "username cisco privilege 15 secret 5 $1$..\nusername test privilege 15 secret 5 $1$.."
}

TASK [Check that 'test' is in stdout_lines (wrong)] ***************************************************************************************************************************************************************
skipping: [localhost]

TASK [Check that 'test' is not in stdout_line (wrong)] ************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "Did not find 'test' in stdout_lines (but that's probably a lie)"
}

TASK [Check that 'test' is in output (good)] **********************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "Found 'test' in entire output"
}

TASK [Check that 'test' is not in output (good)] ******************************************************************************************************************************************************************
skipping: [localhost]

PLAY RECAP ********************************************************************************************************************************************************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0    skipped=2    rescued=0    ignored=0

$ ansible-playbook /tmp/test.yml 
test user (yes/no): : no

PLAY [localhost] **************************************************************************************************************************************************************************************************

TASK [shell] ******************************************************************************************************************************************************************************************************
ok: [localhost]

TASK [debug registered vars we will use] **************************************************************************************************************************************************************************
ok: [localhost] => (item=username_contents.stdout_lines) => {
    "ansible_loop_var": "item",
    "item": "username_contents.stdout_lines",
    "username_contents.stdout_lines": [
        "username cisco privilege 15 secret 5 $1$..",
        "username toto privilege 15 secret 5 $1$.."
    ]
}
ok: [localhost] => (item=username_contents.stdout) => {
    "ansible_loop_var": "item",
    "item": "username_contents.stdout",
    "username_contents.stdout": "username cisco privilege 15 secret 5 $1$..\nusername toto privilege 15 secret 5 $1$.."
}

TASK [Check that 'test' is in stdout_lines (wrong)] ***************************************************************************************************************************************************************
skipping: [localhost]

TASK [Check that 'test' is not in stdout_line (wrong)] ************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "Did not find 'test' in stdout_lines (but that's probably a lie)"
}

TASK [Check that 'test' is in output (good)] **********************************************************************************************************************************************************************
skipping: [localhost]

TASK [Check that 'test' is not in output (good)] ******************************************************************************************************************************************************************
ok: [localhost] => {
    "msg": "Did not find 'test' in entire output"
}

PLAY RECAP ********************************************************************************************************************************************************************************************************
localhost                  : ok=4    changed=0    unreachable=0    failed=0    skipped=2    rescued=0    ignored=0

Which version of ansible are your using and which version of the jinja2 library ? Try to update.

$ ansible --version
ansible 2.9.7
config file = None
configured module search path = ['/home/user/.ansible/plugins/modules', '/usr/share/ansible/plugins/modules']
ansible python module location = /usr/local/lib/python3.6/dist-packages/ansible
executable location = /usr/local/bin/ansible
python version = 3.6.9 (default, Apr 18 2020, 01:56:04) [GCC 8.4.0]

$ pip list | grep Jinja2
Jinja2 2.11.2

Other (weird) things you can try:

Quote your entire test and remove parenthesis.
when: "'test' in username_contents.stdout"

Change for the search test:
when: username_contents.stdout is search('test')

I really appreciate your help, thanks! So this one works: when: username_contents.stdout is search('test').
I may found a issue. When ansible generates output, it creates a list. That's why this doesn't work in my case too: username_contents.stdout.find('test') != -1

Error:
fatal: [r5]: FAILED! => {"msg": "The conditional check 'username_contents.stdout.find(usr) != -1' failed. The error was: error while evaluating conditional (username_contents.stdout.find(usr) != -1): 'list object' has no attribute 'find'\n\nThe error appears to be in '/var/production/Cisco/configure_ospf/g_facts_copy.yml': line 23, column 5, but may\nbe elsewhere in the file depending on the exact syntax problem.\n\nThe offending line appears to be:\n\n\n - name: check if user exists\n ^ here\n"}

Even though I've tried using python interpretation for finding string in list/dictionary when: usr in username_contents['stdout'] but no luck so I'm guessing it's Ansible bug.