Is it permissible to use the monetary value of a vow to purchase items for the mosque, such as "books for the library and clogs for the bathroom," instead of donating it as "a sum of money"?

You must fulfill the vow as you intended, so give the amount to the mosque's supervisor to purchase what is most beneficial for the mosque. If there is no supervisor, then you should buy for the mosque what you deem most beneficial and suitable. If what you mentioned is indeed the most suitable and beneficial for the mosque, then there is no harm in purchasing it with the vowed amount.