The business wouldn’t be illegal, because no physical good or money going in or out would be in violation of the host country’s laws. And exactly what happens i

The business wouldn’t be illegal, because no physical good or money going in or out would be in violation of the host country’s laws. And exactly what happens inside the embassy isn’t under the host country’s purview, since the embassy grounds belong to the diplomat’s country and are subject to its laws only. If the host country doesn’t like what they suspect is happening inside an embassy, they can go through diplomatic channels to request it be terminated (perhaps with a threat of some kind, like expulsion of the diplomat).