There aren’t any examples of state run businesses this old, right? It seems like at 1,500 years governments aren’t robust enough to survive. So any business run by a government would not survive the political upheavals.
The organization has existed and has had a need to find funding for it's activities. Since the question was about 'state' run entities, the goal of "making a profit" seemed not particular salient.
Honestly, I thought the more contentious part of this claim was going to be if the Church of Sinai constituted a state.
That is not as contentious, because it's basically autocephalous/self governing.
It's always been a couple dozen loners in the Sinai peninsula maintaining self sufficiency, which is why I don't find it a good example - as there are plenty of similarly old and continuous organizations, but never truly scaled.