en.wikipedia.org/wiki/Giuseppe_Pecci

The page attributes the creation of the academy to the encyclical Aeterni Patris of 4 August 1879. But the Holy See’s own documents show that the academy was created later, in a separate measure.

• The official text of Aeterni Patris is an encyclical "On the Restoration of Christian Philosophy" dated 4 August 1879. It discusses the renewal of philosophy, especially in the Thomistic tradition, but it is not the act that establishes the academy.
• The Holy See’s official page for the Pontifical Academy of St. Thomas Aquinas states that the academy "was established on 15 October 1879 by Leo XIII."
• Leo XIII’s letter Iampridem considerando of 15 October 1879 explicitly says, in Italian, "Conseguentemente decidiamo di istituire in Roma un'Accademia..." ("Consequently, we decide to establish in Rome an Academy..."). That is the founding act.

So the academy may have followed from the program announced in Aeterni Patris, but saying that the encyclical itself "created" it is inaccurate.

The number in this sentence is off by an order of magnitude, and the description of access is overstated.

According to the Vatican Library’s official history:

• Under Leo XIII, the Library was opened to a larger public of researchers and historians.
• In 1892, the current Reading Room for Printed Books was opened.
• A Vatican Library historical presentation specifies that in that room "trentamila volumi"—that is, 30,000 volumes—were placed directly at scholars’ disposal.

So the official Vatican sources contradict the article’s claim of a consultation library of 300,000 volumes, and they describe access as being broadened for researchers and historians rather than thrown open to the "general public."