I think the primary issue here is not so much anxiety as lack of knowledge. OP apparently does not know the basics of how water comes into and exits a house.
This actually doesn't surprise me. It's not taught in schools, as far as I know. A lot of people think "open tap, water comes out; flush loo, poo goes away", and they don't ever feel the need to learn more than that. It will be taken care of by someone else.
Now OP has seen a scary notice. Some of the words on it have reminded her of another story that she vaguely remembers about something bad happening, in which those words featured. Most of us don't encounter the words "septic tank" very often. (It sounds like a tank with a wound that's got infected, ewww.)
I suspect that this lack of knowledge is actually quite common, especially among people who were not encouraged to explore the workings of the world around them very much as children.
When I was 6 or 7 we went on holiday. There was a stream on the beach and all the kids would try to build dams to hold the water back. But the water always overflowed in the end, which made sense because there was more and more water arriving. But that got me thinking, how could a tap could turn water off and it then didn't overflow, or swell and burst the pipe like in cartoons. After all, there was a lot more water coming down that pipe too, wasn't there, so why didn't it work like the stream? I can't remember how old I was when I learned about how pressure works, but it was definitely quite a way along in science classes. And again, it wasn't explained in terms of domestic taps.
So I think the thread could be a bit kinder to OP. She has got to adulthood without really understanding how the water supply works, and she's reacting badly to being confronted with that lack of knowledge in an unfamiliar situation. None of that seems worthy of criticism to me.