Ivory Search not working on product categories pages on translated site

Dear community,

I am having an issue with the translated pages of our site when searching for product categories pages using Ivory Search.

The categories do appear on the original site in French by typing either part or the full name; with the translated sites, managed by TranslatePress plugin, categories will only show by typing one letter but will disappear if one keeps typing the full name.

See examples here:

Working in French https://snipboard.io/tXSnzD.jpg

only working by typing one letter in italian: https://snipboard.io/Y1G7CP.jpg

not working in italian (no results found) https://snipboard.io/mRfWI8.jpg

Additionally, a part of the URL generated by Ivorysearch on the translated page by TranslatePress doesn’t get translated: https://snipboard.io/q89Ui7.jpg

Could you advice?

The page I need help with: [log in to see the link]