Allow users to edit their own comments through REST API.

allow-users-to-edit-their-comments.php

<?php
add_filter( 'user_has_cap', 'bea_add_edit_comment', 10, 4 );
/**
 * Allow users to edit their own comments
 *
 * @param array   $allcaps An array of all the user's capabilities.
 * @param array   $caps    Actual capabilities for meta capability.
 * @param array   $args    Optional parameters passed to has_cap(), typically object ID.
 * @param \WP_User $user    The user object.
 *
 * @return mixed
 */
function bea_add_edit_comment( $allcaps, $caps, $args, $user ) {
  // As working with REST Api only
  if ( ! defined( 'REST_REQUEST' ) || true !== REST_REQUEST ) {
  	return $allcaps;
  }
  
  // Always allow the user to moderate comments
  if ( in_array( 'moderate_comments', $caps ) ) {
  	$allcaps['moderate_comments'] = true;
  	return $allcaps;
  }
  
  // Only modify user capabilities if we are trying to edit a comment
  if ( 'edit_comment' !== $args[0] ) {
  	return $allcaps;
  }
  
  /*
   * We need to be sure we have three arguments
   * $args[0] => the capability we want to allow for the user
   * $args[1] => the current user id
   * $args[2] => the current comment id
   */
  if ( count( $args ) < 3 ) {
  	return $allcaps;
  }
  
  // We need a valid comment
  $comment = get_comment( $args[2] );
  if ( is_null( $comment ) ) {
  	return $allcaps;
  }
  
  /*
   * We are checking if the current user are the one who wrote
   * the current comment. If it's the case then add the required
   * permissions for the edit process to succeed
   */
  if ( Functions::user_can_manage_comment( $comment, $user->ID ) ) {
  	$allcaps['edit_others_posts'] = true;
  	$allcaps['edit_published_posts'] = true;
  }
  
  return $allcaps;
}

Hi @sharcupine, sorry for the delay ! I never get any notification for your answer.

You right, my bad I pasted it too quickly, in my code it was into a class, but when sharing on gist it should not be wrapped into a class, so I messed up ^^
Anyway I fixed my gist and now fully working, thx for the "issue" 👍