From whatis.com:
"A birdie is a false, or phantom, signal that appears in a superheterodyne
wireless receiver. Birdies are internally generated, resulting from the outputs of the oscillators that form part of the receiver circuit. They usually sound like unmodulated carriers -- signals with "dead air." Occasionally they are modulated by clicks, humming sounds, or audible tones.
Birdies can occur as a result of the receiver being tuned to a
frequency that is a multiple of the output frequency of one of the internal oscillators. These signals are known as harmonics. A birdie might also be heard at a frequency corresponding to the sum or the difference of the internal
oscillator frequencies. These signals are called mixing products. Birdies are inevitable in any superheterodyne wireless receiver. However, in a well-engineered receiver, most or all of the birdies occur at frequencies outside the normal range of operation, so they have little or no detrimental effect on receiver performance.
A birdie is not the same thing as a spurious response. If a receiver picks up a signal whose transmitter is operating at a frequency other than that to which the receiver is tuned, the
modulation of the unwanted signal will be heard or decoded. In some cases, two or more strong external signals can combine in a receiver's radio-frequency amplifier, causing numerous spurious responses. This phenomenon, called intermodulation ("intermod"), can be a problem in downtown metropolitan areas where many wireless transmitters operate simultaneously."
ALL superhet receivers have birdies, but in good quality radios, they are minimized to the point that a good signal on the frequency in question will overcome them. They generally are not caused by the power supply. More likely the microprocessor or synthesizer. I'm not saying that the power supply can't produce noise in the RX, just not usually birdies.
I really wonder if WireWeasel actually has a birdie. Interference yes, birdie maybe not. Is it still there if you disconnect the antenna? If not, then it's probably not an internally generated noise.