Various ways of adding classes to anchors, as well as title markup within that anchor, from hook_preprocess_field in Drupal 8. These are all link fields, which do not have a base twig to modify the output of the a tag.

mytheme.theme

<?php

/**
 * Implements hook_preprocess_field().
 */
function mytheme_preprocess_field(&$variables) {
  if ($variables['element']['#entity_type'] == 'paragraph' && $variables['field_name'] == 'field_reference_link') {
    foreach ($variables['items'] as $key => $item) {
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__link-tag';
    }
  }

  if ($variables['field_name'] == 'field_directions_link') {
    foreach ($variables['items'] as $key => $item) {
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__link-tag';
    }
  }

  if ($variables['field_name'] == 'field_my_top_guides') {
    foreach ($variables['items'] as $key => $item) {
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__link-tag';
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__link-tag--with-arrow';

      $variables['items'][$key]['content']['#title'] = new FormattableMarkup('<span>@title</span>', [
        '@title' => $item['content']['#title'],
      ]);
    }
  }

  if ($variables['field_name'] == 'field_external_service_link') {
    foreach ($variables['items'] as $key => $item) {
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__button';
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__button--small';
      $variables['items'][$key]['content']['#options']['attributes']['class'][] = 'hl__button--minor';
    }
  }
}