This phrasing oversells it a bit too much: The water wasn't a power source and there was no long distance movement of it.
They signaled between users with the light of a burning handheld torch, and the duration of the light corresponded to predefined messages.
Water was used at each end for independent stopwatches, to measure the duration of the light. It's easy to imagine an equivalent system using sand hourglasses.
https://en.m.wikipedia.org/wiki/Hydraulic_telegraph#Greek_hy...
I just asked chatgpt “Based on what you know about me, what do you think I would be interested in seeing in Athens?”
The Herakleidon Museum was third on the list. May have to try this again in the future.
Annoyingly I’m in Athens right now but flying back tomorrow way too early to sneak a visit in :(