How to save and load configuration data of type sequence

I have a theme “basic_theme”. I want to add some settings to this theme, in particular config menu_search_fields is a sequence of data, each entry has 3 informations (field, weight and uuid).

I’m pretty sure the schema is correct because I almost copied from coremodulesimageconfigschemaimage.schema.yml

basic_theme.settings:
  type: theme_settings
  label: Basic theme settings
  mapping:
    menu_search_fields:
      type: sequence
      label: Menu search fields
      sequence:
        type: mapping
        mapping:
          field:
            type: string
          weight:
            type: float
          uuid:
            type: string

Inside theme-settings.php I have some fields to map to those data, for example field “field” is:

$i = 0; // for this example only one entry
$form('menu_search')('fields')('wrapper')($i)('field-wrapper')(
    "menu_search_fields.$i.field"
) = (
    '#type' => 'textfield',
    '#title' => t('Field'),
    '#default_value' => theme_get_setting(
        "menu_search_fields.$i.field"
    ),
);

I used as a key “menu_search_fields.$i.field” but i doesn’t work.

How can I correctly map the fields with sequence entries?