Implement ThirdPartySettingsInterface in contact module for contact form config entity

Over all I am RTBC on this issue but I don't know a lot about ThirdPartySettings.

+++ b/core/modules/contact/tests/modules/contact_storage_test/contact_storage_test.module
@@ -38,3 +40,45 @@ function contact_storage_test_entity_type_alter(array &$entity_types) {
+/**
+ * Implements hook_form_FORM_ID_alter() for contact_form_edit_form().
+ */
+function contact_storage_test_form_contact_form_edit_form_alter(&$form, FormStateInterface $form_state) {
+  contact_storage_test_contact_form_alter($form, $form_state);
+}

there should be a "contact_form_form" base form ID too, should save you two methods?

The schema for the pony is missing in the test module. You can test that pretty easily, there's a trait and a few lines of code that you copy & paste and it will automatically validate all the config of your test. See Drupal\config\Tests\DefaultConfigTest.

Maybe adding this we could find an actual usage?
For example refactor "send a copy" or add "set a text" or path alias?

+++ b/core/modules/contact/config/schema/contact.schema.yml
@@ -22,6 +22,11 @@ contact.form.*:
+    third_party_settings:
...
+        - type: node_type.third_party.[%key]

any reason to add dependency on node module?

Actual use cases only make sense in third party modules, if we add something to core, it will just live in contact.module.

Yeah, that should be contact_form.third_party.[%key] :)

Would be great to add the schema validation trait stuff to make sure this is actually working :)

Looks great!
PS: would be great to update summary to point and example what this for could be needed

Possible examples:
1) settings for advanced notifications and redirect #306662: Add redirect option to site-wide contact forms
2) rules integrations could mark contact for some special processing

I'd love to help on this one but the code is way out of my league. D8 is hard.

Looks good. Committed f48a467 and pushed to 8.0.x. Thanks!