I’ve made a fresh local install and “kávé” worked OK but some other words did not. It seems the problem is related to the full text search in PostgreSQL and how the text is parsed. For example from search word “kávé” will be “ká” after normalization and that normalized form will be matched to the text so “kávé” and “káposzta” are both correct results for the FTS 
I hope the situation will improve with using hunspell dictionaries in PostgreSQL but currently the Hungarian one is broken 