Can this be CM related noise?
The ultrasonic sensor needs HIGH CURRENTS during transmit. Since the measurement errors show up even with Just The Ground connected, this suggests some power_rail filtering will improve/lower the transient noise floor. That filter needs a capacitor and an inductor.

You need a large capacitor, located within 1mm (that is, very very close) to the GND and VDD pins of the ultrasonic sensor. The purpose is to locally provide the high transient charge demands.

You need a "LOCAL BATTERY" for the ultrasonic sensor; that requires a shunt capacitor and a series impedance. Because of high transmit energy, I'd use 100uF across GND/VDD. And for the series impedance, I'd use 1uH or 10uH.

The capacitor and inductor, together, form a voltage_divider.

Here is the "LOCAL BATTERY" in a circuit







simulate this circuit &ndash; Schematic created using CircuitLab