Water leak

Is it water or coolant? Where is it leaking, inside on the passenger side floor or on the ground? By "started again" do you mean it was leaking as soon as you got out of the car or after it sat for a while and cooled down?

There's some confusion. If you had the cooling system tested it should be leaking coolant, not water, unless you only have water in the cooling system. If that's the case, water doesn't have the same seal conditioners and water pump lubricant that is in antifreeze. That alone could lead to a leak. If it is indeed the cooling system that's leaking and it's near the front of the engine, the water pump is the most likely suspect, especially given that it leaks when it cools down. The lip seal around the shaft will balloon up and seal better when pressure builds up in the system. It will relax and open up and leak when there's no pressure.

No. The seal conditioner additives in antifreeze will keep seals in good condition but it won't fix those that are already leaking. First you said it leaked a lot when it cooled off, now you're saying there's no leak when it cools down. It could be the level is down below the point of the leak at times so no additional leak will show up, and it's possible for a seal to stop leaking when it's warm because pressure that builds up in the system holds the seal against its sealing surface. I'm still inclined to suspect the water pump. One thing you can do is to fill the coolant, (water is okay at this point), then drive the car far enough to warm it up. Disassemble the front of the engine to get to the water pump, then inspect the area with a black light. The dye will show up as a bright yellow stain that you can follow up to the source of the leak.

Once the leak is solved, install a 50/50 mix of antifreeze and water. The antifreeze contains corrosion inhibitors, seal conditioners, and water pump lubricant. Those additives wear out over about a two-year period which is why replacing the antifreeze is a part of normal maintenance.

After rereading my previous reply, I have to clarify that you can add a bottle of dark purple dye to the cooling system, THEN drive it a while, then check for bright yellow stains with a black light.

A water pump does normally leak all the time, but it is also common for some to not leak when the engine is warm. It depends on how it fails. If the rubber lip seal wears out, it can expand and seal when warm or when the normal pressure buildup pushes the seal against the spinning shaft. Seal failure is most common when running just water in the system. Antifreeze contains seal conditioners, water pump lubricant, and corrosion preventers.

If the bearings wear out they will let the water pump's shaft wobble and move away from the lip seal. The drive belt holds the shaft off-center so it will leak all the time. Nothing will solve that except replacement of the pump.