The Holy See's most recent consolidated budget and balance sheet disclosure (2020) states an overall Roman Curia patrimony of about four billion euros, naming the Vatican Museums and the Vatican bank as contributors, but no source found in this pass breaks the total down by individual Curia institution, so a wealth value cannot be attested for the Vatican Apostolic Library or the Vatican Observatory specifically.
What would resolve this A future Holy See financial disclosure, or independent Vatican-finance reporting, that itemizes the consolidated patrimony by institution rather than reporting one aggregate figure.
OpenVatican finance / canon law administrationThe Associated Press, Vatican Releases Budget, Balance Sheet Amid Financial Scandal (Associated Press via Al Jazeera, 2020)