“Only one of the eight water systems has any public faucets”.
I’m really confused about “any” here. I can’t catch it, so please explain its usage here.
Thank you.

It refers to an amount or a number of something, however large or small.

In this case, the sentence explains that there are no public faucets in seven of the systems. It is an alternative to:
Only one of the eight water systems has a public faucet.

Did you think about looking this up independently in a dictionary?
oxfordlearnersdictionaries.c … ny_1?q=any

If not, why not?