GET method form is not processed
I could solve the problem myself, based on this solution for Drupal 7.

Instead calling the form directly in the router, I define a page callback in my_module.routing.yml.

my_module.form:
  path: '/my-module-form'
  defaults:
    _title: 'My module form'
    _controller: '\Drupal\my_module\Controller\MyModuleController::searchForm'


In MyModuleController, I load my form via the builder.

public function searchForm() {

  $form_state = new FormState();
  $form_state-&gt;setMethod('get');
  $form_state-&gt;setAlwaysProcess(TRUE);
  $form_state-&gt;setRebuild();

  $form = \Drupal::formBuilder()-&gt;buildForm('Drupal\my_module\Form\MyModuleSearchForm', $form_state);
  unset($form['form_build_id']);
  unset($form['form_id']);

  return $form;
}


The code of form then is like in the question above.