Overriding an existing filter

This is the pattern for a filter.

Applying/using a filter on something:

$filtered_version = apply_filters( 'the name of the filter', $the_thing_being_filtered );

This is how you use a filter to modify something:

add_filter(
    'the name of the filter', 
    'name_of_a_function_that_will_modify_the_thing_being_filtered'
);

function name_of_a_function_that_will_modify_the_thing_being_filtered( $the_thing_being_filtered ) {
    // modify $the_thing_being_filtered here
    return $the_thing_being_filtered;
}

So in your examples it did not work because category_dropdown is not the name of the filter, edd_category_dropdown is the name and they do not match so they do not work.

Order also matters, you can’t add a filter to something after it has happened without some form or time travel. WP won’t wait until all filters and actions/hooks are added then evaluate it at the end, that’s not how PHP works.

tech