New translation system with twig problem (prestashop 1.7.6.0)

[KoMmEn]

Hi, so basically my problem is that translations have no effect in my back office pages. I tried to do simple module, currently
working on prestashop 1.7.6.0. I'm using new translations system with domain Modules.Nameofmymodule.Admin for all sentences in the BO.
When I get into 'Translations' -> 'Modify translations' section and select my module I get all of the sentences that I want to translate.
They're properly saved to the db (ps_translations). The problem is that they're not working at all on my twig pages. Fun fact is that displayName
and the description of my module is translated properly, but my twig page content is not. Tried to clear cache etc., but still facing this problem.
Does anyone know what am I missing? Any help would be really appreciated

EDIT: From what I could see translations via php code ($this->trans(..)) works fine, but translations via twig are not

Edited October 4, 2021 by KoMmEn (see edit history)