I would use the plane mesh approach for , start by creating a mesh plane that covers the width of trench cut into the landscape.
Then you will want to create a spline ‘road tool’ (just use a water material instead of asphalt) similar to the one in tutorial by . When you have it complete it will automatically place plane meshes along a spline so you can create bends in the river.
For the material you will want to use a “Panner” node along with a couple of normal maps to create the water movement, I believe the built in Lake material shows an example of , you will want to increase the speed along one axis to make it look like the water is moving (you can download the project in my signature below if you want as well, it has some panning normal maps). Beyond that you can try using Flowmaps as well, but they are a bit more complex.
is actually something I have been meaning to try out with my material as well, if I get something working here I’ll let you know. 