Allow non-Author to edit & save a published wordpress post. This works around issues with `_wp_translate_postdata` & `user_has_cap` - Fixes "Sorry, you are not allowed to edit posts as this user."

wp-edit_published_posts-fix.php

<?php
/*
 *
 * ALLOW USER TO EDIT POST IF THEY ARE SELECTED AS THE PM
 * Preferred way would be to use `user_has_cap` - see:
 *  - https://wordpress.stackexchange.com/a/360990/5380
 *  - https://developer.wordpress.org/reference/hooks/user_has_cap/
 * However, WordPress has a nasty long standing issue with this line:
 *  - https://bit.ly/3I72jOn
 * Where it forces a check to make sure the author is current user, which prevents any efforts to customize capabilities by using a `user_has_cap` filter. The bug is documented here:
 *  - https://core.trac.wordpress.org/ticket/30452
 *  - https://wordpress.stackexchange.com/a/186280/5380
 * So instead we're getting very hacky and maniuplating how WP checks capabilites:
 *  - https://core.trac.wordpress.org/ticket/30452#comment:3
 * By modifiying code from @danielbachhuber:
 *  - https://gist.github.com/danielbachhuber/18850d571c5dce419f8b
 * Which he created for his plugin, Co-Authors Plus (which might be the better option than the code below)
 *  - https://wordpress.org/plugins/co-authors-plus/
 *
 */
function filter_map_meta_cap_allow_nonauthor_to_save_post( $caps, $cap, $user_id, $args ) {
  // Adapted from @danielbachhuber : https://gist.github.com/danielbachhuber/18850d571c5dce419f8b
  // To solve issue with `_wp_translate_postdata` : https://core.trac.wordpress.org/ticket/30452#comment:4
  global $pagenow;
  switch ( $cap ) {
    case 'edit_post':
    case 'edit_others_posts':
      $post_obj = false;
      if ( 'edit_post' === $cap ) {
        $post_obj = get_post( (int) $args[0] );
        /* Allow original authors to 'edit_others_posts' when updating
         * Addresses core bug in _wp_translate_postdata()
         *
         * @see https://core.trac.wordpress.org/ticket/30452
         */
      } else if ( 'edit_others_posts' === $cap
        && 'post.php' === $pagenow
        && ! empty( $_POST['post_ID'] ) ) {
        $post_obj = get_post( (int) $_POST['post_ID'] );
      }
      if ( ! $post_obj ) {
        break;
      }

      $post_type = get_post_type($post_obj);
      $post_author = $post_obj->post_author;
      $post_ID = $post_obj->ID;

      // Allow user to edit the post based on custom meta
      if ( 'custom-job' == $post_type ) {

        // My custom meta is saved on a MetaBox.io custom taxonomy field
        // you'll want to replace all the code below to check if your user should have access

        // retrieve the term object from the job/post
        $jobsTable = ['storage_type' => 'custom_table', 'table' => 'custom_jobs'];
        $pm_term_obj = rwmb_get_value('job_pm_taxonomy', $jobsTable, $post_ID);
        $pm_term_id  = $pm_term_obj->term_id;

        // retrieve the user id from the related term meta
        $pm_user_id = get_term_meta( $pm_term_id, 'pm_related_user', true ); 
    
        // check if the pm user account id matches the current logged in user id
        $currentUserID = wp_get_current_user()->ID;
        if ($pm_user_id == $currentUserID) {
          // Don't require editing others' posts
          if ( false !== ( $key = array_search( 'edit_others_posts', $caps ) ) ) {
            unset( $caps[ $key ] );
          }
          // If the post is published...
          if ( 'publish' == get_post_status($post_obj)) {
            $caps[] = 'edit_published_posts';
          } elseif ( 'trash' == get_post_status($post_obj)) {
            if ( 'publish' == get_post_meta( $post_ID, '_wp_trash_meta_status', true ) ) {
              $caps[] = 'edit_published_posts';
            }
          } else {
            // If the post is draft...
            $caps[] = 'edit_posts';
          }
        }
        break;
      }
  }
  return $caps;
}

add_filter( 'map_meta_cap', 'filter_map_meta_cap_allow_nonauthor_to_save_post', 10, 4 );

@brandonjp You saved my day, thankyou!