third_party_settings in THEME.settings.yml cannot be dependency managed

Patch for 10.1.x.

I think I've got a related problem: My module has theme-specific settings. Previously I just my modules config settings into the root of theme.settings.yml. Inspired by the shortcut module, I now wanted to clean this up and move it into third party settings. Basically I wanted to update my config from

third_party_settings:
  shortcut:
    module_link: true
tailwind_jit:
  compile_html_requests: true
  html_input_file: 'foo.css'
  compile_ajax_requests: true
  ajax_input_file: 'bar.css'

to a proper schema

theme_settings.third_party.tailwind_jit:
  type: mapping
  label: 'Tailwind JIT settings'
  mapping:
    compile_html_requests:
      type: boolean
      label: 'Compile HTML requests'
    html_input_file:
      type: path
      label: 'Uncompiled CSS input file for HTML requests'
    compile_ajax_requests:
      type: boolean
      label: 'Compile Ajax requests'
    ajax_input_file:
      type: path
      label: 'Uncompiled CSS input file for Ajax requests'

and proper third party settings

third_party_settings:
  shortcut:
    module_link: true
  tailwind_jit:
    compile_html_requests: true
    html_input_file: 'foo.css'
    compile_ajax_requests: true
    ajax_input_file: 'bar.css'

The form hook is something like

function tailwind_jit_form_system_theme_settings_alter(&$form, FormStateInterface $form_state, $form_id = NULL) {
  $form['third_party_settings']['tailwind_jit'] = [
    '#type' => 'details',
    '#open' => TRUE,
    '#title' => t('Tailwind CSS Just-in-time compilation'),
    '#tree' => TRUE,
    '#parents' => ['third_party_settings', 'tailwind_jit'],
  ];
  $form['third_party_settings']['tailwind_jit']['compile_html_requests'] = [
    '#type' => 'checkbox',
    '#title' => t('Compile HTML requests'),
    '#default_value' => theme_get_setting('third_party_settings.tailwind_jit.compile_html_requests', $themeToBeConfigured),
  ];
  /* ...more form elements here... */
}

This does not work correctly, there are two problems:
1) The schema is not used/validated, the boolean value is still stored as (int) 0 / 1 and not as (bool) true / false
2) When submitting the form, it saves all my values, but wipes the existing config from shortcut module.

Reading @berdir's comment, is shortcut a bad example? Should I avoid third party settings for themes at all?