Hi, I live in Lisbon, so I might help clarify the issue
Some years ago the restaurants/bars were in a crisis and become annoyed with people asking for tap water with ice cubes and not consuming anything else, so they started denying it.
As of 2021 there is a law that says that restaurants/bars/cafés have to provide free glasses of tap water to clients. However, if you are not a client, then it is a choice of the establishment to give the free glass of water or not. For non clients there is no law prohibiting it, but there is no law enforcing it either.
Most establishments will give the free glass of water unless they are very busy or are located in a area with many tourists (which can be the case of some places in the Senda Litoral during summer months). Many bars/cafés will even have glasses and a water jar for people to serve themselves. Choose bars/cafés over restaurants
And btw, you are saying it correctly. A "copo de água" usually refers to a glass of water, not a bottle. If you want to reinforce the idea just say "copo de água da torneira"
Bueno Camino!