$siblings = $this->menuLinkManager->getChildIds($parent->getPluginId());
But main question is how to get MenuLinkContent when I have that MenuLinkInterface object?
There are two types of plugin IDs. Without or with a colon :
.
Non-derived plugins
Without they point directly to a single plugin definition.
For example the admin menu
\Drupal::service('plugin.manager.menu.link')->getChildIds('system.admin');
consists mainly of non-derived menu links which IDs you find in *.links.menu.yml files.
Derived plugins
With colon the first part is the base plugin ID and the second part is the derivative ID.
For example, if you have created a multi-level main menu from UI and apply this command on a menu parent
\Drupal::service('plugin.manager.menu.link')->getChildIds('standard.front_page');
You get links like this
menu_link_content:421a421a-cb1d-33e7-a810-1e7341f7906b
for the base plugin MenuLinkContent (BTW also defined in a YAML file) with a deriver for MenuLinkContent entities (identified by UUID).
$entity = \Drupal::service('entity.repository')
->loadEntityByUuid('menu_link_content', '421a421a-cb1d-33e7-a810-1e7341f7906b');
If you have already a plugin instance you can get the UUID from the plugin object. See https://drupal.stackexchange.com/a/235769/47547