Entity Base Field can't be saved as empty string from form (including as default)

Problem/Motivation

It should be possible to save the empty string '' on a non-compulsory string entity base field.

Create a field on an entity:

     $fields['string_field'] = BaseFieldDefinition::create('string')
        ->setLabel(t('Non-compulsory string field'))
        ->setDefaultValue('')
        ->setRequired(FALSE);

This will allow you to enter the field empty.

WidgetBase::extractFormValues() {
line 371: $items->setValue($values);
// Adds the blank item
372: $items->filterEmptyItems();
// Filters out the empty items.
// So the field list is an empty array.
}

So by this point $entity->fields['string_field']['x-default']->list = [];. This gets retrieved and cast to NULL before saving the entity, causing an SQL Integrity constraint violation: 1048 Column 'string_field'; cannot be null rather than saving a Default value.

Possibly related #2567899: Empty node titles cause failures when migrating because empty strings are treated as NULL → although not cause by removing the value when extracting the values from a form.

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes