The water disc has only 1 face (the cap) with normal up — good. But the vertices are at (0,7,0.25) — that's radius 7 centered at origin (0,0). The pond center is at (8,-7), but the water disc is at (0,0)! The water disc was created centered at the origin, but the pond depression is at (8,-7). The water disc location is (0,0,0) — it doesn't cover the pond!

I need to move the water disc to (8,-7,0). Let me fix that.

import bpy, os, tempfile
import numpy as np
from mathutils import Vector
from bpy_extras.object_utils import world_to_camera_view

pond = bpy.data.objects['PondWater']
pond.location = (8.0, -7.0, 0.0)
print('pond moved to', pond.location)

# restore water material
mat = bpy.data.materials.get('WaterMat')
bsdf = mat.node_tree.nodes['Principled BSDF']
bsdf.inputs['Base Color'].default_value = (0.10, 0.22, 0.20, 1.0)
bsdf.inputs['Transmission Weight'].default_value = 1.0
bsdf.inputs['Roughness'].default_value = 0.04

out = os.path.join(tempfile.gettempdir(), 'check_water.png')
bpy.context.scene.render.filepath = out
bpy.ops.render.render(write_still=True)
print('rendered', out, os.path.getsize(out))

img = bpy.data.images.load(out)
w, h = img.size
px = np.array(img.pixels[:], dtype=float).reshape((h, w, 4))[..., :3]
cam = bpy.data.objects['Camera']
scene = bpy.context.scene
for xyz, label in [((8,-7,0.25),'pond_center'), ((8,-3,0.25),'pond_north'), ((5,-5,0.25),'pond_west')]:
    v = world_to_camera_view(scene, cam, Vector(xyz))
    if 0 <= v.x <= 1 and 0 <= v.y <= 1:
        col = int(v.x*w); row = int((1-v.y)*h)
        print(label, (round(v.x,3), round(v.y,3)), 'rgb', px[row,col].round(3))
    else:
        print(label, 'off', (round(v.x,3), round(v.y,3)))
bpy.data.images.remove(img)