Proof of Concept (PoC) - so mostly incomplete and untested code - how a PHP wrapper for Impfterminservice could look like.
require_once 'impftermine.class.php';
// replace "my-unique-appname" with an unique name for your application
$impftermine = new Impftermine("my-unique-appname");
// get available vaccines
$res = $impftermine->getVaccines();
// get vaccination centers
$res = $impftermine->getVaccinationCenters();
// get vaccination center details
$res = $impftermine->getVaccinationCenter(PLZ);
// get appointment availibility by vaccination center (= PLZ)
$res = $impftermine->getAvailbilityByVaccinationCenter(PLZ);