It is much more accurate if you use the pump. I tried just measuring the pressure in the tube from the water column, it was all over the board and the resolution sucked, probably 10X worse. Using the pump fixes that because you aren’t just measuring how much the water compresses the air, you’re measuring exactly what pressure it takes to push out the bottom, which is exactly the water column. It doesn’t take much of a pump if all you’re pressing against is a few feet of water. Something like this: https://www.aliexpress.com/item/1005009288427024.html

I’d just tie it to a heavy nut and drop it in the well. I probably wouldn’t even measure it, just calibrate on some known water levels and watch it for a while.