The story was quickly picked up everywhere, from the Jerusalem Post to Géo. Yet on closer inspection, the claim may seem surprising: for centuries, editions of the Conics have included Books V and VII, based precisely on an Arabic translation. The celebrated Edmund Halley produced a complete edition, even including a reconstruction of Book VIII, which really was lost.
So what happened? It all stems from a recently published volume cited by every article in question: Prophets, Poets and Scholars: The Collections of the Middle Eastern Library of Leiden University, a scholarly book published by Leiden University.
The volume contains a chapter by the mathematician and historian of science Jan Pieter Hogendijk entitled Jacobus Golius and his Arabic manuscripts on the exact sciences. It discusses the collection of Arabic manuscripts acquired by Jacob Golius in the 17th century. This collection does indeed include the Arabic translation of Apollonius—an important means of accessing the text at the time, but one that is perfectly well known today.
The book makes absolutely no claim that the manuscripts have been rediscovered—it is a very serious work—but apparently the first journalist to make that mistake passed it on to fellow journalists. Proof that fake news can find its way into mathematics and its history too!