First you need to understand the difference between NULL and "empty".
NULL is the absence of a value. Any (or at least almost any) data type can be NULL. When you have a column of type integer, and you don't want to put a value in that field, you put NULL.
"Empty" is a string/text concept. It's a string with an empty value, i.e. ''. A text field with an empty string contains a value: the empty string. It is not the same as containing NULL, i.e. no value. Other data types e.g. integer, boolean, json, whatever, can't have an empty string.
Now to COALESCE. That function works on any data type, and basically it returns the first not-NULL result of its arguments. So COALESCE(NULL, TRUE) returns TRUE because the first argument is NULL; COALESCE(FALSE, TRUE) returns FALSE because the first argument is not NULL; and COALESCE(NULL, NULL) returns NULL because there are no not-NULL arguments.
So, COALESCE(field, '') returns the value of field if it's not NULL, and otherwise returns an empty string. When used in COALESCE(field, '') = '' when trying to find any rows where field is "empty", this is basically saying "if field is NULL then use an empty string in its place, then see if it equals an empty string". This is because NULL and an empty string are not equivalent, and "you" are trying to find any rows where fields are NULL or empty.
In your version of the query, where you just do field = '', that will ONLY return results where field is actually an empty string, not where field is NULL. Which behaviour you desire is up to you.