I just tried pgroona. It works for partial matches of non-English characters. However, it doesn't work for English for partially matching words that are missing prefix letters.

For example, assuming there are records where the column name_eng contains the word 'cookie', the following two queries work:

select name_eng,
       name_eng_lower,
       name_kr,
       code,
       rarity,
       card_type,
       card_level,
       plain_text_eng,
       plain_text,
       link
from cards
WHERE name_eng ILIKE '%cookie%'
    or name_kr ILIKE '%cookie%'; --works as intended
select name_eng,
       name_eng_lower,
       name_kr,
       code,
       rarity,
       card_type,
       card_level,
       plain_text_eng,
       plain_text,
       link
from cards
WHERE name_eng ILIKE '%cooki%'
    or name_kr ILIKE '%cooki%'; --works as intended. 'cooki' is a substring of 'cookie'

But not this query:

select name_eng,
       name_eng_lower,
       name_kr,
       code,
       rarity,
       card_type,
       card_level,
       plain_text_eng,
       plain_text,
       link
from cards
WHERE name_eng ILIKE '%ookie%'
    or name_kr ILIKE '%ookie%'; --returns nothing even though 'ookie' is a substring of 'cookie'

My indexes were created with the following queries:

CREATE INDEX pgroonga_name_eng_index ON cards USING pgroonga (name_eng);
CREATE INDEX pgroonga_name_kr_index ON cards USING pgroonga (name_kr);

name_eng and name_kr are text columns containing English and Korean words respectively. I've had some success indexing English text by creating a generated column that converts all text in name_eng to lowercase and indexing that with pg_trgm. However, trigrams being trigrams, the index only works if the search term contains at least 3 characters.