I found another feature of this bug. If I switch the forum language to English, I see a new value "Item tagline", and it is the same as on the item editing page. If I switch the language on the forum back to Russian, I see the old value on the forum and the new value on the edit page. I think your plugin is only in English, so you don't see any problems. Maybe the problem has something to do with the phrase system you wrote about above?
Can you also tell me where the value of this field is stored, in which table and the name of the column? I didn't find such a column in the xf_dbtech_shop_item table.