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After checking you module provided for me on git, I fix it with

$fields['date'] = BaseFieldDefinition::create('created')
  ->setLabel(t('DateTime'))
  ->setDescription(t('Date and time.'))
  ->setDisplayOptions('view', array(
    'label' => 'above',
    'type' => 'timestamp',
    'weight' => -4,
  ))
  ->setDisplayOptions('form', array(
    'type' => 'datetime_timestamp',
    'weight' => -4,
  ))
  ->setDisplayConfigurable('form', TRUE)
  ->setDisplayConfigurable('view', TRUE);

and get following results

After checking your module provided for me on github and some reverse-engineering I find out the problem is on create('datetime') and you should use create('created') So the following code

$fields['date'] = BaseFieldDefinition::create('created')
  ->setLabel(t('DateTime'))
  ->setDescription(t('Date and time.'))
  ->setDisplayOptions('view', array(
    'label' => 'above',
    'type' => 'timestamp',
    'weight' => -4,
  ))
  ->setDisplayOptions('form', array(
    'type' => 'datetime_timestamp',
    'weight' => -4,
  ))
  ->setDisplayConfigurable('form', TRUE)
  ->setDisplayConfigurable('view', TRUE);

Results the below image for me. it seems it's Ok now.

Try to set

  ->setDisplayOptions('view', array(
    'label' => 'hidden',
    'type' => 'timestamp',
    'weight' => 0,
  ))
  ->setDisplayOptions('form', array(
    'type' => 'datetime_timestamp',
    'weight' => 10,
  ))

After checking you module provided for me on git, I fix it with

$fields['date'] = BaseFieldDefinition::create('created')
  ->setLabel(t('DateTime'))
  ->setDescription(t('Date and time.'))
  ->setDisplayOptions('view', array(
    'label' => 'above',
    'type' => 'timestamp',
    'weight' => -4,
  ))
  ->setDisplayOptions('form', array(
    'type' => 'datetime_timestamp',
    'weight' => -4,
  ))
  ->setDisplayConfigurable('form', TRUE)
  ->setDisplayConfigurable('view', TRUE);

and get following results

Try to set

  ->setDisplayOptions('view', array(
    'label' => 'above',
    'type' => 'timestamp',
    'weight' => -4,
  ))

Try to set

  ->setDisplayOptions('view', array(
    'label' => 'hidden',
    'type' => 'timestamp',
    'weight' => 0,
  ))
  ->setDisplayOptions('form', array(
    'type' => 'datetime_timestamp',
    'weight' => 10,
  ))