Content entity form not displaying the previously selected value
You need to set a default value for the field. Drupal's field system by default assumes a field is empty, you will have to manually add a default value to the field definition. 

This default value should be based on your entity's value, or be an empty string or NULL in case there is no value yet. Try something like this:

// Use the entity value if available, or NULL otherwise.
$default_value = !empty($entity-&gt;my_value) ? $entity-&gt;my_value : NULL;
$fields['content_display'] = BaseFieldDefinition::create('list_integer')
  -&gt;setDisplayOptions('form', [
    'type' =&gt; 'options_buttons',
    'weight' =&gt; -4,
   ])
  -&gt;setCardinality(BaseFieldDefinition::CARDINALITY_UNLIMITED)
  -&gt;setSetting('allowed_values', $values)
  -&gt;setDisplayConfigurable('form', TRUE);

  // Set the default value on the field.
  -&gt;setDefaultValue($default_value);