2
There’s no need to change host right away, you can install the mysql56 module which gives support up to at least Drupal 9.3.
Support won’t continue forever, so it would be a good idea to start making plans to move to a host with more up to date software.
1
You are only using the wrong property name for passing the user ID.
The following would work:
$entities = \Drupal::entityTypeManager()
->getStorage('node')
->loadByProperties([
'type' => 'article',
'uid' => SOME_USER_ID,
]);
If you wish to fetch entities from several users, just use an array:
$entities = \Drupal::...
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