You can translate badge text only. Visibility, background color, text color, and priority are shared across languages.
Translate as follows.
(1) Open the selling period rule
Open the selling period rule to translate.
(2) Open the translation screen
Select "Translate," then choose a language.
(3) Enter the translation and save
Under "Product card badge text," enter the translations for before, during, and after the selling period, then select "Save."