The old magnetron Wx radar transmitter's output was on the order of 60 KW, pulsed, for an average power of about 600 watts, like the microwave in your kitchen, just at higher frequency.
Solid state radar transmitters, introduced in about 1980, have 75-150 watts pulsed power, or less than 1 watt average power, even in doppler turbulence detection mode.
I rank Wx radar effect on birds in the same category as Wx radar attracting lightning.
You're most likely to get a wrong evasive reaction from birds if you're approaching them from below, as their quickest escape is to pull in the wings and dive.
GB