RuntimeException: Failed to start the session because headers have already been sent

Some more information.
I configured cron to run every hour.
The problem occurs only when a user is logged on and the cron task runs because the last cron run was more then an hour old.
When I trigger the cron task from the admin menu...there is no problem.
Also when there is no user logged on and cron runs... there is no problem.

This is the code.
<?php

namespace Drupal\fjmodule\Plugin\QueueWorker;

use Drupal\Core\Queue\QueueWorkerBase;

/**
* Processes tasks for example module.
*
* @QueueWorker(
* id = "url_queue",
* title = @Translation("Example: Queue worker"),
* cron = {"time" = 5}
* )
*/
class UrlQueue extends QueueWorkerBase {

/**
* {@inheritdoc}
*/
public function processItem($item) {
$url = $item->url;
\Drupal::logger('fjmodule_queue_cron')->notice("Start ".$url);
$store = \Drupal::service('tempstore.shared')->get('fjmodule.urls');
\Drupal::logger('fjmodule_queue_cron')->notice("End ".$url);
$info = [];
$info['time_last_verified'] = REQUEST_TIME;
$info['result'] = $verificationResult;
// The key can only be 128 Chars.
$store->set(substr($url, 0, 128), $info);
return;
}
}

This is an extract of the recent log messages

cron 11/20/2021 - 18:49 RuntimeException: Failed to start the session because… Anonymous (not verified)
fjmodule_queue_cron 11/20/2021 - 18:49 Start https://www.google.be/maps/place/ALDI/@50.7822688… Anonymous (not verified)
cron 11/20/2021 - 18:49 RuntimeException: Failed to start the session because… Anonymous (not verified)
fjmodule_queue_cron 11/20/2021 - 18:49 Start https://www.google.be/maps/place/Lidl/@50.779345,… Anonymous (not verified)
cron 11/20/2021 - 18:49 RuntimeException: Failed to start the session because… Anonymous (not verified)
fjmodule_queue_cron 11/20/2021 - 18:49 Start https://www.google.be/maps/place/Albert+Heijn/@50… Anonymous (not verified)

I want to test that a series of url's used somewhere on the site are still valid.
If they are... I store the last verification time in the tempstore.

Yes, this is only a part of the code... but the problem is in the tempstore line.
When I input a certain url in a webform, I must be capable to get the last verified time.
So I thought that tempstore.shared was the easiest way to handle this.
What do you mean with key value...

Replacing
$store = \Drupal::service('tempstore.shared')->get('fjmodule.urls');
by
$store = \Drupal::service('keyvalue.expirable')->get('fjmodule.urls');
solves the problem... no more errors.
Thanks for the suggestion.