Extracts small api_get/api_post helpers to cut the repeated curl/header/
json.loads boilerplate, then uses them for a new subtest that creates a
client, invoices it, marks the invoice sent, and pays it in full - checking
the invoice comes back paid with a zero balance. Runs after the PDF preview
check, since PreviewController::blankEntity only builds its mock PDF when
the company has no invoices/invitations yet.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>