How to evaluate a when condition for Ansible task

No need to use regex for pattern searching. You can use search like this:

when: name_prefix | search("stage-dbs")

It will definitely work.

Not sure filter search exists today?

solution with https://docs.ansible.com/ansible/latest/user_guide/playbooks_filters.html#searching-strings-with-regular-expressions :

when: name_prefix | regex_search("^stage-dbs(.*)$")