Banding happens because the sky contains too few distinct tonal values, especially in an 8-bit file. After strong adjustments, smooth gradients get rounded into visible steps (posterization). Blur usually just smears those steps; it doesn’t create missing tonal data. Noise can help because it adds random variation, but too much will look coarse.

Better approaches:

• Work in 16-bit/channel if possible before making major tonal edits. This gives more headroom and reduces rounding artifacts during adjustment.
• Make gentler, fewer adjustments rather than repeated heavy edits that keep re-rounding values.
• Check whether one channel has more usable detail than another. In a blue sky, the blue channel may be nearly maxed out, so red or green may contain smoother tonal information that can sometimes be used in a mask or blend.
• If banding is already present, a very small amount of noise/dither is the standard fix; there isn’t a perfect way to recreate missing tones after they’re gone.

So the key is prevention: use higher bit depth and less destructive editing, and only add subtle noise as a last step if needed.