Interesting choice to emulate the colors of the Renaissance painters. Generally paintings from that time have a very yellow, orange cast to them. Is there a particular painting you were referencing? I'd love to see it.
I'm a big fan of incorporating painterly theory into digital post processing. Painters are masters of leading the eye, implying detail, and making imagery that's feels in general pleasing to look at. One of the main things Renaissance painters do is compress the shadow detail, so your imagination fills it in . I can tell you're on the right path with how you've processed this image.
As for the critique, the first thing that stands out is the lack of low frequency texture. When the LF texture gets too smoothed, it tends to have that blurry-yet-sharp look that isn't nice to look at. This is especially evident when the image is downsized or viewed as a thumbnail. I think the best way to work on LF texture is with gentle d&b. Smoothing filters and mixer brush take a VERY controlled hand to apply believably.
Overall the contours of the face are reading nice and clear, but there are some spots that draw my eye. Attaching a gif so you can see what I'm seeing.
Great job NOT removing the lower half of her eyeball (some people mistakenly think these are eye bags). But there are some actual undereye darkness that should be reduced (see gif).
Finally there's some strange subtle color patches happening. Under her eyes are orange, her shoulder has greens, and her forehead has pink. I'd select those areas and use selective color to push the hue to where it doesn't stand out.
Really appreciate the contribution, looking forward to more from you. I can tell you've got the mind of an artist. And imo artists make the best retouchers.