Hi Levy I have tried to reproduce the banding effect that you show and have finally managed but only by mangling my files. I started with a moon just before dawn RAW shot that was properly exposed. I reduced the resolution as banding will be more apparent with a smaller file. No matter what I did I could not reproduce the banding. I darkened it 3 stops converted it to a jpeg reprocessed it lightening it the 3 stops put in elliptical lightening far more than you seem to have, exported it to facebook, reimported it and still no banding in photoshop but I can see it on this site. Note nobody would do this to an image.
View attachment 15798
In this case I started with a recent file that I had deliberately underexposed by 4 stops. Again a moonshot just before dawn. I reduced the resolution and brightened it 4 stops in RAW, no banding. So with the banded image posted below with a 4 stop underexposed shot I converted it to a jpeg brightened it by 4 stops and obtained banding. No real surprise an 8 bit file has 256 levels 4 stops underexposed it has only 16 levels so a smooth gradation will be banded into no more than 16 levels and that if it goes from white to black since it doesn't the banding will be more extreme. Personally I don't often find banding to be a major problem in facebook, sharpening and edges are a major problem everyone may have different views.
View attachment 15799
So what does this tell us. If the file started as a properly exposed RAW file and the lightening of the sky happened in ACR ot Lightroom (ie as a 12/14/16 bit file then I can't see how this happens. If the file started as an underexposed 12/14/16bit RAW file then I still can't really see how you get banding lightening it in Photoshop or Lightroom. If however you start with an underexposed jpeg or do the lightening as an 8 bit file then it is easy to get banding. I have kept clear of the mathematics but am willing to go into it but all too often people use mathematics the same way that a drunk uses a lampost "for support not illumination". It may be a good case for letting this community loose on the RAW file as a challenge, I would certainly enjoy it. I hope that this helps even if in a negative way. Ken