Drupal - How to print taxonomy term field in node.html.twig?

To get the field value from a field in a taxonomy term that is referenced in the node:

{{ node.field_example.entity.field_desired_field.value }}

If you want to render a formatted output, use either the ui to configure a custom view mode or use the module Twig Tweak:

{% set tid = node.field_example.target_id %}
{% if tid %}
  {{ drupal_field('field_desired_field', 'taxonomy_term', tid) }}
{% endif %}