On earth and what we witness through natural science and our direct reality.
Water finds level
Water will not conform to the exterior of a shape
There is more to it than water finds its own level. The Panama Canal shows us that water from the Pacific Ocean finds its own level as it dumps into the Gulf of Mexico, via the Panama Canal. But the Canal is needed, because the Ocean and the Gulf are not of the same level, even though they are connected around North and South America. So, regarding FE, water doesn't find its own level, and yet it does. This means that it is not an example that can be used to support FE.
Stick almost any object into water, and pull it out again. When you do, the object is wet. Where is the object wet? On its exterior, of course. So you see that water most often conforms to the exterior shape of an object.
In addition, all you need to do is walk out into the water on a beach. Notice that the beach is not level. Notice that out where the water is deep, there is still water at the bottom of the water. In other words, water absolutely does conform to the exterior shape of the bottom of the ocean that it covers.
Just a fyi I have never stated the earth is flat. I in all honesty have no proof regarding the shape of the earth.
I will state that NASA is showing us bullshit imagery and videos shot from within the ISS.
I will also state we are not living on an oblate spheroid that is the size that is claimed.
What happens to the water as it drips off the object? It falls and finds its level. Yes there is surface tension. There is also meniscus. I don't find your example legit. Mainstream science has figured that out and I am on board with surface tension and meniscus. If you can show us a body of water, say 100 gallons, do this and then stick to the exterior of the surface then you would have something.
The last paragraph is a bit like WTF. The ocean floor is the container. The water is INSIDE the container not on the OUTSIDE. Sea level on the east coast of NA - Sea level on west coast of England. Middle of the Atlantic in between the 2 destinations is deeper than sea level. Same thing happens with a cup of water. Your example is a false equivalence. Practically demonstrate a BODY of water sticking to the EXTERIOR of a surface.