How to use tsvector_update_trigger with jsonb column?
You don't.  You will need to write your own trigger function.  The built in one only works for text columns, not for jsonb columns and not for functions over columns.
On newer versions, an alternative would be use a generated column.
create table tags (
    translations jsonb, 
    tsv tsvector generated always as (to_tsvector('pg_catalog.english',translations#&gt;&gt;'{en,name}')) stored 
);