I don't think that publicly funding water makes it a human right. Society has just collectively decided to make it a public good in your example.

But if some human walks up to my front door and demands water, they have no inherent right that says I must provide it to them. As the commenter stated, that would impose upon me a force against my will, hence violating my rights of private property.

Let's take that example a step further: If someone could come to my house and demand water and I wad compelled to provide them with it, what would stop them from setting up a water bottling operation, of which I am funding?

It sounds like you're describing the argument of positive rights vs. negative rights. Then couldn't water rights be expressed as "people cannot be deprived of access to clean and potable water"?

Correct, I am describing exactly that.

And to your point, I would agree, but only insofar as the water that people are not being denied access to is not privately owned.

For example, you taking water out of the ocean, desalting it, and then consuming it is perfectly fine. Nobody owns the ocean. You haven't violated anyone's property rights. Me being forced to give you water that I have paid for would be a violation of my property rights, thus it would be deemed a positive right, and rights in the US are not positive.

This is the same for housing. Nobody should be denied the use of their private property as they see fit (zoning laws would be a consideration upon purchase). Thus, housing is a negative right in that nobody would stop anyone from setting up a tent or living nomadically on their own property. This already exists today!

The problem comes into play when people try to institute positive rights on housing which either force someone into an involuntary transaction through providing time/resources to build someone else a house or via forcing them to allow people to use their privately held land as a camping site.

So what happens to the people who don't have property? Do they lose the right to exist in every particular place? Do they, then, lose the right to life itself? Or, if they sleep somewhere forbidden, does society grant a positive right to freedom from the nuisances of theft, vagrancy, and public defecation -- protections provided by public funds through police and prisons?

There are bounties of people with wealth that gladly give charitably. Many organizations, especially religious institutions, exist with a core mission of helping the impoverished. Why everyone pushes the responsibility of helping their community off to the government is beyond me, especially given the clowfare which are our politicians. Nobody would ever give them the reigns to a business because hardly any of them have experience in business.

Could more be done, of course! But the problem is that the government keeps requiring people to give them money so they can do the job, which leaves everyone else worse off since government never spends more efficiently than the private sector. I lose ~30% of my income immediately. Think what could be done with it if I were to allocate it instead of the government.

Not having property is not proper justification for violating the rights of others.

Edit: let me tack on that nobody benefits from impoverished citizens. They are a net drag as they need supporting either through charity or through social programs. It is in everyone's best interest to help end it, but of course you cannot violate the rights of others which means you cannot forcibly hold a mentally sick person against their will, for example. The problem with social programs is everyone shrugs off the duty because "the government is fixing it" while ignoring the whole of the moral hazard each and every new government program creates.

Buy some land and drill your well for water. Nothing preventing water access.