Just like individuals enter agreements with publishers in order to print and disseminate their works, so does the Holy See. IIRC, it has its own publishing house that it uses for a limited range of its publishing (e.g. Latin or Italian language), but for foreign work it contracts with local publishers. Being “publisher to the Holy See” doesn’t make a company an organ of that state, only an employee. Still, just like any other form of business, landing a high profile client is a great way to generate business through the consumer confidence that can engender, much like a law firm would advertise itself as “attorneys to the royal family.” Hence the self-advertisement of the Catholic publishers.