I'm a beginner with D8 but wrote own modules in D7. It is therefore possible that I miss some understanding to get easily what I need. All hints to help me step ahead are appreciated.

When I add a comment field to a node entity I have the possibility to configure for anonymous users between the following options:

See CommentItem.php

function fieldSettingsForm(array $form, FormStateInterface $form_state) ( ...
     $element['anonymous'] = array(
      '#type' => 'select',
      '#title' => t('Anonymous commenting'),
      '#default_value' => $settings['anonymous'],
      '#options' => array(
        COMMENT_ANONYMOUS_MAYNOT_CONTACT => t('Anonymous posters may not enter their contact information'),
        COMMENT_ANONYMOUS_MAY_CONTACT => t('Anonymous posters may leave their contact information'),
        COMMENT_ANONYMOUS_MUST_CONTACT => t('Anonymous posters must leave their contact information'),
      ),
      '#access' => $anonymous_user->hasPermission('post comments'),
    );

In CommentForm.php

function form()...
    // Add author email and homepage fields depending on the current user.
    $form['author']['mail'] = array(
      '#type' => 'email',
      '#title' => $this->t('Email'),
      '#default_value' => $comment->getAuthorEmail(),
      '#required' => ($this->currentUser->isAnonymous() && $anonymous_contact == COMMENT_ANONYMOUS_MUST_CONTACT),
      '#maxlength' => 64,
      '#size' => 30,
      '#description' => $this->t('The content of this field is kept private and will not be shown publicly.'),
      '#access' => ($comment->getOwner()->isAnonymous() && $is_admin) || ($this->currentUser->isAnonymous() && $anonymous_contact != COMMENT_ANONYMOUS_MAYNOT_CONTACT),
    );

    $form['author']['homepage'] = array(
      '#type' => 'url',
      '#title' => $this->t('Homepage'),
      '#default_value' => $comment->getHomepage(),
      '#maxlength' => 255,
      '#size' => 30,
      '#access' => $is_admin || ($this->currentUser->isAnonymous() && $anonymous_contact != COMMENT_ANONYMOUS_MAYNOT_CONTACT),
    );

I see the COMMENT_ANNONYMOUS_MAY_CONTACT or COMMENT_ANONYMOUS_MUST_CONTACT is used to set the field access option and the COMMENT_ANONYMOUS_MUST_CONTACT is used to set the field required option. Therefore it is not possible to set the configuration in such I way to get rid of the homepage field, since this is accessible and not required in both cases.

In my case I want to have the contact information where the name and e-mail are required without the homepage field. Unfortunately there is no possibility to change this within the manage field tab.

I thought the best solution would be to have the possibility to make show up the fields name, e-mail and homepage in the manage form display tab as soon as the value in the comment settings form is set to either COMMENT_ANONYMOUS_MUST_CONTACT or COMMENT_ANONYMOUS_MAY_CONTACT in order to set them as deactivated if not needed.

The idea was to use hook_entity_base_field_info_alter() to set the homepage field with ..->setDisplayConfigurable('form', TRUE) to become configurable. But this does not seem to work. In addition I see in entity.api.php several warings about upcoming needed changes.

Current solution is to use

function hook_form_comment_comment_form_alter(&$form, Drupal\Core\Form\FormStateInterface $form_state, $form_id) {
  $form['author']['homepage']['#access'] = FALSE;
}

I think that others would appreciate to have this ability too and maybe there should be added a change request into core. Looking at this I don't really know where this change request should be added (comment module? field entity? content entity? other?). Any suggestions are appreciated