The idea behind this format is to gain the advantages of short query strings that you have with comma and separator formats while marking a field as explicitly an array via a postfixed [] syntax.

import queryString from 'query-string'

queryString.stringify({ foo: ['one'] }, { arrayFormat: 'bracket-separator' })
// => foo[]=one

queryString.stringify({ foo: ['one', 'two', '', 'four' ] }, { arrayFormat: 'bracket-separator' })
// => foo[]=one,two,,four

queryString.stringify({ foo: ['one', 'two', '', 'four'] }, { arrayFormat: 'bracket-separator', arrayFormatSeparator: '|' })
// => foo[]=one|two||four

queryString.parse('?foo[]=one', { arrayFormat: 'bracket-separator' })
// => {foo: ['one']

queryString.parse('?foo[]=one,two,,four', { arrayFormat: 'bracket-separator' })
// => {foo: ['one', 'two', '', 'four']}

queryString.parse('?foo[]=one|two||four', { arrayFormat: 'bracket-separator', arrayFormatSeparator: '|' })
// => {foo: ['one', 'two', '', 'four']}

There are still are 2 question in regards to implementation:

What should happen for {foo: []}? Currently, it would drop the parameter from the stringified query which is the same as {foo: null}

This is undesirable personally. I feel like {foo: []} should produce ?foo[] unless I specify a flag to drop it.
This would be a deviation from the ?bar&biz that non-arrays get the treatment of when they are null (no trailing =), but I feel like it makes sense as we have enough information to say, explicitly, that this is an array. Whereas if it were {foo: null} we don't know, explicitly, that this is an array, so it would produce ?foo which would mean that it would roundtrip correctly.
However, the only way to produce this would be to change how the system is using Array.prototype.reduce as the reducer function is not ever invoked when the array is empty.

What should happen for {foo: ['one', null, 'three']}. Currently it will drop the null and produce foo[]=one,three

I haven't a strong opinion on this as it matches the functionality of separator. The only deviation from the separator functionality in regards to value dropping is that bracket-separator does not drop empty strings.