Access (none related) entities from within twig without preprocessing

Drupal twig prevents you from a few functions, but you can add custom functionality via a custom twig extension, let's say get_any_node_field_value

in twig:

<div>
  {{get_any_node_field_value(nodeId, 'field_my_custom_name')}}
</div>

This article appears to give a good introduction into setting up a custom twig extension. In a nutshell:

web/modules/custom/your_module/src/Extension/TwigExtension.php:

<?php

namespace Drupal\your_module\Extension;

use Twig\Extension\AbstractExtension;
use Twig\TwigFunction;

class TwigExtension extends AbstractExtension {

  public function getFunctions(): array {
    return [
      new TwigFunction('get_any_node_field_value', [$this, 'get_any_node_field_value']),
    ];


    public function get_any_node_field_value ($nodeId, $fieldName) {
      // your logic goes here  
    }

}

Please keep in mind, that this does not effect your cache settings, so you will not get automatic template updates, if the unrelated node X changed. Depending on your usecase this might not be an issue, but it might fall on your toes later. If you need to care about caching, it's better to go via the preprocess and extend also the cache tags.