Currently, November 2023, when using the 'Product type' filter with Shopify Search & Discovery app, it only functions in a store's default language and will be hidden in a non default language. This is being worked on and we estimate that product type will be fully translatable for the start of 2024.
In the mean time, this is a workaround to achieve much the same functionality, plus the ability to translate. It does it by creating a metafield that holds the same values, and metafields have translation support. Please note, the original problem of product type not being translatable will be solved; if you use this workaround you would later be wanting to delete it and switch back. So this is only suggested as a short term fix to cover the gap.