Different front page per language
Technically, the config override API that config translation uses allows any kind of override of configuration.
The core config translation however only does translation, meaning it only allows to change things that are classified as user-facing texts and not technical strings.
What you want is usually referred to as localization, changing things based the language that isn't actually a &quot;translation&quot;. There is a core issue to better support this, https://www.drupal.org/node/2275865, but it hasn't been updated in quite some time.
There are a few possible workarounds, though:

Since you mention nodes, in Drupal 8, translations of nodes have the same ID/URL. That means you could have your different front pages as translations of the same node. That would be problematic if you use Paragraphs for example, as that doesn't currently support translatable fields, so you'd be forced into the same structure.

You could use Page Manager to have different front pages (there is a per-language constraint necessary, which has a patch but has not yet been committed) or even just a view that selects a node based on a certain condition (like filtered by language of a certain type).

A custom callback that displays a certain node based on a bit of code.


Update:
4 years later, I had this use case too and still no activity on the core issue. As a workaround, I altered the config schema and made the front_page a label type to be able to translate it. Not fully tested yet, so beware of dragons:
function custom_config_schema_info_alter(&amp;$definitions) {
  // Change the front page type to label so that it can be translated.
  $definitions['system.site']['mapping']['page']['mapping']['front']['type'] = 'label';
}