Diagnosis
This is coil whine from the camera's internal power supply circuitry. It is a known hardware issue with some units. The noise is often more audible in a silent room.
How to Fix It
Contact eufy support directly. This is generally considered a defect if the unit is new. They will likely request a video of the noise for verification. Be prepared to provide your purchase receipt and serial number. They typically offer a replacement camera unit under warranty.
If That Didn't Work
If a replacement is not possible, you can attempt to dampen the sound. The noise emanates from the back of the camera. Mounting the camera on a soft surface, like a felt pad, can slightly reduce resonance. Do not open the camera casing.
Heads Up
Do not confuse this with the normal, very faint operational hum of the camera lens focusing. Coil whine is distinctly high-pitched and tonal, like a faint whistle or squeal.