My ultrasonic water tank node (pro-mini+rfm69) is now 2 years on the same 2xAA batteries sending in levels every hour (RTC), the only problem encountered - condensation forming a drip on the face of the ultrasonic head during very low temperatures.

Perhaps you should first ask yourself why you want to communicate with the gateway by wire?

The sketch you have found to work with the ultrasonic sensor, normally sends its data via the radio module.
This can be replaced by a serial protocol transport to the gateway, but you will have to write that yourself on both sides, both on the arduino and on the gateway.
There are plenty of examples of code where arduino's talk to each other via the serial ports. On the Pi side you will also have to implement the same serial protocol.
On the hardware side, you must take into account that the distance between the arduino and the Pi, is limited. The arduino and the Pi use a serial signal based on 5V. Be careful with arduino's that run on 3.3V, you will need to put a converter in between. If you want to bridge long distances, you will have to go to an RS485 implementation and not a serial RS232 implementation.

Probably you want a wired solution because of the water tank.
I've read already topics about it, I even think on this forum, about people who did build something equivalent.
You can maybe search first other topics about this to get ideas of building this type of sensor.

I read the other topic and I think that I know what I'm doing wrong. I want to connect a sensor to the gateway but stil want the Arduino in between because of the nice script I found.

So my question should be is it possible to connect a Arduino with sensor to a raspberry gateway by wired connection?

I a sketch of what I mean.