fix: Identifier not persisted on customer created via Inbox API Channel (#5804)

- Fixes the identifier not being used to identify the contact, this results in having a new contact created every time the email or phone is not supplied.

Fixes: #5704

spec/controllers/public/api/v1/inbox/contacts_controller_spec.rb

@@ -15,6 +15,15 @@ RSpec.describe 'Public Inbox Contacts API', type: :request do
       expect(data['source_id']).not_to be_nil
       expect(data['pubsub_token']).not_to be_nil
     end
+
+    it 'persists the identifier of the contact' do
+      identifier = 'contact-identifier'
+      post "/public/api/v1/inboxes/#{api_channel.identifier}/contacts", params: { identifier: identifier }
+
+      expect(response).to have_http_status(:success)
+      db_contact = api_channel.account.contacts.find_by(identifier: identifier)
+      expect(db_contact).not_to be_nil
+    end
   end
 
   describe 'GET /public/api/v1/inboxes/{identifier}/contact/{source_id}' do