list of supported value in entity baseFieldDefinitions setDisplayOptions type(field widget) I'm new in Drupal, I create my first entity and use baseFieldDefinitions to set fields and in fields I use setDisplayOptions to set form like this:

$fields['piece'] = BaseFieldDefinition::create('integer')
  -&gt;setLabel(t('piece'))
  -&gt;setDisplayOptions('view', [
    'label' =&gt; 'hidden',
    'type' =&gt; 'string',
    'weight' =&gt; 2,
  ])
  -&gt;setDisplayOptions('form', [
    'label' =&gt; 'inline',
    'type' =&gt; 'string',/////// what is supported value list of type key
    'weight' =&gt; 2,
  ])
  -&gt;setDisplayConfigurable('form', TRUE)
  -&gt;setDisplayConfigurable('view', TRUE);


what is supported value list of type key in display option?

I only found options_buttons and string
What you are looking for are the field widget plugins, these depend on what modules you have installed.

Use Drupal Console to run this command:

drupal debug:plugin field.widget


This is what I have on a local site with some contrib modules:

 -------------------------------------------- --------------------------------------------------------------------------------------- 
  Plugin ID                                    Plugin class                                                                           
 -------------------------------------------- --------------------------------------------------------------------------------------- 
  boolean_checkbox                             Drupal\Core\Field\Plugin\Field\FieldWidget\BooleanCheckboxWidget                       
  datetime_datelist                            Drupal\datetime\Plugin\Field\FieldWidget\DateTimeDatelistWidget                        
  datetime_default                             Drupal\datetime\Plugin\Field\FieldWidget\DateTimeDefaultWidget                         
  datetime_timestamp                           Drupal\Core\Datetime\Plugin\Field\FieldWidget\TimestampDatetimeWidget                  
  email_default                                Drupal\Core\Field\Plugin\Field\FieldWidget\EmailDefaultWidget                          
  entity_reference_autocomplete                Drupal\Core\Field\Plugin\Field\FieldWidget\EntityReferenceAutocompleteWidget           
  entity_reference_autocomplete_tags           Drupal\Core\Field\Plugin\Field\FieldWidget\EntityReferenceAutocompleteTagsWidget       
  field_example_3text                          Drupal\field_example\Plugin\Field\FieldWidget\Text3Widget                              
  field_example_colorpicker                    Drupal\field_example\Plugin\Field\FieldWidget\ColorPickerWidget                        
  field_example_text                           Drupal\field_example\Plugin\Field\FieldWidget\TextWidget                               
  field_permission_example_widget              Drupal\field_permission_example\Plugin\Field\FieldWidget\TextWidget                    
  file_generic                                 Drupal\file\Plugin\Field\FieldWidget\FileWidget                                        
  image_image                                  Drupal\image\Plugin\Field\FieldWidget\ImageWidget                                      
  language_select                              Drupal\Core\Field\Plugin\Field\FieldWidget\LanguageSelectWidget                        
  link_default                                 Drupal\link\Plugin\Field\FieldWidget\LinkWidget                                        
  menu_item_extras_view_mode_selector_select   Drupal\menu_item_extras\Plugin\Field\FieldWidget\MenuItemExtrasViewModeSelectorSelect  
  moderation_state_default                     Drupal\content_moderation\Plugin\Field\FieldWidget\ModerationStateWidget               
  number                                       Drupal\Core\Field\Plugin\Field\FieldWidget\NumberWidget                                
  oembed_textfield                             Drupal\media\Plugin\Field\FieldWidget\OEmbedWidget                                     
  options_buttons                              Drupal\Core\Field\Plugin\Field\FieldWidget\OptionsButtonsWidget                        
  options_select                               Drupal\Core\Field\Plugin\Field\FieldWidget\OptionsSelectWidget                         
  path                                         Drupal\path\Plugin\Field\FieldWidget\PathWidget                                        
  string_textarea                              Drupal\Core\Field\Plugin\Field\FieldWidget\StringTextareaWidget                        
  string_textfield                             Drupal\Core\Field\Plugin\Field\FieldWidget\StringTextfieldWidget                       
  text_textarea                                Drupal\text\Plugin\Field\FieldWidget\TextareaWidget                                    
  text_textarea_with_summary                   Drupal\text\Plugin\Field\FieldWidget\TextareaWithSummaryWidget                         
  text_textfield                               Drupal\text\Plugin\Field\FieldWidget\TextfieldWidget                                   
  uri                                          Drupal\Core\Field\Plugin\Field\FieldWidget\UriWidget                                   
 -------------------------------------------- ---------------------------------------------------------------------------------------