When it comes to PORTRAIT RETOUCHING in post processing, I suppose, I can write a book-not a manual on how to do it but about all the debatable issues and why it is difficult to critique any example unless the work was obviously poorly performed.
Given a certain level of basic skill, it all has to do with the extent of the retouching. When a retouched or even a soft focus of diffused portrait appears on this forum there are folks who will opine that it is good job- well done. Others will say that it is insufficiently corrected OR may will say there is too much softening etc. Any of theses opinions may be valid, however, they all forgot about the most important opinion, that of the subject. Which leaves to yet another question; who decides what to do, the photographer or the subject? Please see the next paragraph
So...who is the arbiter of retouching aesthetics? As a "COMMERCIAL" portrait photographer, it is my job to find our what the client expects. Some clients assume that when they come to a professional photographer and pay good money, he or she is gonna show them at their best and make them look good, otherwise they can go to a hobbyist friend or do a selfie. Some folks will tell me that they don't care and "let it all hang out", that is, until they see an unflattering proof and then request "plastic surgery" be done to their portrait. Some require "plastic surgery" from the get go- they tell me right off the bat! Few, perhaps some gentlemen and actors may prefer a "character study" with little or no retouching or even emphasis on wrinkles, lines and skin texture.
Before arranging a portrait session, I always do a pre-sitting consultation to discuses the aesthetics as well as the purpose and style of the portrait and other preparations such as makeup, hair, styling, clothing, colors and choices. With the right preparations, the need for radical retouching can be minimized and issues that can not be adequately addressed in post processing can be dealt with at the camera.
The OP mentions lighting. Retouching in post production can de-emphasize certain undesirable complexion issues, remove some unwanted dermatological conditions such as rashes, blemishes, scars, acne, moles etc, calm down dark circles or "bags" under eyes, sagging skin, a lazy eye etc; however, facial structure and many of the aforementioned issues should be controlled via lighting, posing and camera position. Attempting to do some of this in PP will most likely yield a poor likeness and completely artificial results.
If I ascertain that a significant degree of retouching is going to be necessary, as part of the plan, I will light and shoot accordingly. I may reduce the contrast by adjusting the lighting ratio in that very dense shadow area that is difficult to retouch. I may use a soft-focus lens or filter. If there are deep set eyes, I will make certain that the eyes and the orbital parts of the face are nicely illuminated. If you do not use studio lighting, you can perform many of these lighting adjustments with soft natural light, window light and reflectors.
Retouching itself, of course, pre-dates digital photography. Back in the film era it was done with pencils, dyes, etching knives and bleaches. It was usually a three-stage process. Negative retouching: Density was added to certain areas the negative with special pencils and dyes or reduced by etching or bleaching. Dyes were applied to neutralize certain blemishes- an area of red acne would show up on a color negative a cyan spots so it was neutralized with red dye etc. This was extremely precise and painstaking work and had to be performed by trained an experienced retouches- a spoiled negative could not be repaired- there were no do-overs! Positive retouching was then applied to the print to fill in and blend areas that could not be completely addressed on the negative. This was done with dye, colored pencils, Flexichrome colors and occasionally with airbrush. The third operation was all over or local diffusion at the enlarging stage if required. The negative retoucher had to rely on their experience and skill to pre-visualize the results which would no be completely apparent until the print was produced.
Nowadays, we get to do all of the work at once including other manipulations such as dodging, burning and color correction. Quite the task unless you know what to retouch and what not to retouch, which begs yet another question to be answered.
Back in the day, photographers who did their own retouching and retouching specialists were trained in facial structures and aesthetics. Retouchers had to also have a concept of photography and lighting. It was said that the best retouchers know what not to retouch and when to stop retouching. Oftentimes retouching is done to the extent where the portrait is no longer a true likeness of the subject. Sometimes the tendency is to overdo certain actions, which is especially east to do in digital post production. Usually retouching becomes problematic when it becomes viable and begins to call attention to itself. Always keep the question in mind as to what to retouch and what NOT to retouch. Do not exaggerate eye or teeth whitening, do not alter the shape of the subjects face or features whereby these are no longer authentic or recognizable.
I am pleased when my clients are pleased. When I deliver their portraits and the say "Wow- I do take a good picture"! I NEVER correct them and say I am the one that "TAKES" the pictures around here! I know I did a good job because my work did not call attention to itself and they are pleased with their appearance.
My own philosophy is as follows - you may agree or disagree: Most folks want to be portrayed at their best as they like to appear to others and as they wish to be remembered. I proceed to interpret their wishes accordingly.
As to the OP's image: Not knowing what the subject expected, I did a quick and dirty edit. I tried for a softer approach with more skin correction and left a bit more tonal mass in the background. I wanted a little more separation in the hair/background relationship. I added more negative space in the direction the subject is facing and re-cropped slightly. I dodged the subject's left eye as it was a little obscured in shadow as a result of the broad/Rembrandt lighting in the image.