find if the column of the PostgreSQL table is empty with minimum cost
As far as I know (but not sure), if there are no data at all for the column, there is some property in the database saying that the chunk or the table has no data for this column, at least this happens when adding a new column to the existing table, so the database doesn't update all existing rows if the default value of a new column is NULL

If the row data ends early, it assumes all column after that for that particular row are NULL, or in newer versions, are whatever DEFAULT was at the time the column was added.  But this says nothing at all about what might be in other rows.
You can't avoid scanning the table unless you a had a very strange constraint which forces the values to all be NULL.  But you should be able to scan the table just once, not once for every column.
select count(col1), count(co2), count(col3)...count(col100) from the_table;