Full text search in PostgreSQL with search term including unrelated hyphen and ending
The problem is that the token 'vein-trailer' gets emitted and is located before the bare token 'vein' is, so is between 'code' and 'vein'.

One way to fix this is to make a new text search configuration which doesn't emit hyphenated words:

create text search configuration simple2 (copy=simple);
alter text search configuration simple2 drop mapping for asciihword;


Then the following returns true:

select 
  to_tsvector('simple2','Yakumo Shionome featured in new Code Vein-trailer') 
  @@
  phraseto_tsquery('simple2','Code Vein');


Whether this will fix all your problems, or create new problems, is hard to tell based on your description and also hard to intuit, but it does fix the literal problem you presented.  You probably need to do something with non-ascii hwords as well.