Custom configuration forms: translation access denied
For anyone stumbling towards a similar problem: it seems you have to set-up not only schema, routing and config_translations yml files but you also have to define each configuration in installation yml files so your config is picked up by Drupal.

So I had to include a faq.settings.yml file in /install of my custom module directory, like:

faq_title: ''
faq_text: ''
faq_cta_label: ''
faq_cta: ''
langcode: en


And boom you got yourself a translatable configuration form.