If the top photo isnt lightened as is stands then you have plenty of head room for lightening , in shadow areas there just isn't the literal 'shadows and highlights' which can accentuate the textures of the feathers, just fact of life.
At a thousandth of a sec you had a good number of photons hitting your sensor,
so the grainy look upon lightening is probably largely due to method of lightening.
I don't have your camera so I cant be precise, but if you have lightroom , you can prep your photo initially by shifting the tone curve to amplify the darker areas a bit and then hit it with your usual routine,
but avoid lightening with the regular shadows slider , instead , move it a bit to the Left and lighten the pic overall by raising the 'blacks' slider bringing your darkest areas on the histogram away from the far left .
Like I said , I'm guessing , but will say I routinely shoot a full stop underexposed or more as gauged by the meter ,, which is very misleading in any case,, far better to 'chimp' the shot if you have time.
A different approach would be to just raise the lightness of the colors of the bird which are in shadow in this case mostly orange ,
so you could raise the lightness of the oranges and reds after cooling the color tone of the overall pic from the warm sun ,
OR just check and make sure that the white balance its using is the best one for the colors of the pic to look normal.
Generally , shadows shouldn't look purple upon lightening so you may have some oddness in the ambient reflected light on that street.
Just tossing some ideas out for you to try, up to you to see if you can get em to work for you with your gear.
(There's actually quite a large number of options to reduce the appearance of noise like changing grain size, selective noise reduction , gaussian blur adjustment , unsharp mask , resizing etc with variable levels of effectiveness. )