This is how the church does everything. They never use their resources (other than personnel) to do things, instead they rely on donations and keep their money in their own pockets.
The Church is a body of people. The people of the Church donate money towards its purposes - the preservation of manuscripts isn't a main focus of the Church and is something the support of which isn't confined to Christians (or in this instance Catholics, who may or may not be Christians!).
In the same way that you might donate to a soup kitchen run by a Church fellowship, because the money goes to feeding hungry people, you might donate to manuscript preservation.
That people in the Church donate their time and money towards such causes and ask for other people to donate their money doesn't seem wrong.