How can I get and format the node created date in field.html.twig?
Having a field template you always can get the parent entity via element['#object']. And from there you can get everything else, also the creation timestamp. You then can format it using Twig's date() filter or with format_date() in a predefined Drupal date format.

In any variation of field.html.twig (field--field-myfield.html.twig etc.) do:

&lt;div class="foo"&gt;
  {{ element['#object'].getCreatedTime | date('F j, Y') }}
&lt;/div&gt;

&lt;div class="bar"&gt;
  {{ element['#object'].getCreatedTime | format_date('html_datetime') }}
&lt;/div&gt;




Source: Sample taken from Accessing the original entity in field templates is hard.