Add test for case where existing user have different password

tests/integration/targets/test_mysql_user/tasks/test_update_password.yml

@@ -127,3 +127,25 @@
           update_password: on_create
         - username: test3
           update_password: on_new_username
+
+    # another new user, another new password and multiple existing users with
+    # varying passwords without providing a password
+    - name: update_password | Create account with on_new_username while omit password
+      community.mysql.mysql_user:
+        login_user: '{{ mysql_parameters.login_user }}'
+        login_password: '{{ mysql_parameters.login_password }}'
+        login_host: '{{ mysql_parameters.login_host }}'
+        login_port: '{{ mysql_parameters.login_port }}'
+        state: present
+        name: test3
+        host: '10.10.10.10'
+        update_password: on_new_username
+
+    - name: update_password | Assert create account with on_new_username while omit password produce empty auth string
+      ansible.builtin.command: >-
+        {{ mysql_command }} -BNe "SELECT user, host, plugin, authentication_string
+        FROM mysql.user where user='test3' and host='10.10.10.10'"
+      register: test3_info
+      changed_when: false
+      failed_when:
+        - "'test3\t10.10.10.10\tmysql_native_password\t' != test3_info.stdout"