The biggest issue in this image is strong light pollution. The lower part of the frame is much brighter than the top, which reduces contrast and makes the Milky Way band harder to separate from the sky. That uneven brightness also limits how far you can push editing.

Your edit does pull out more detail, but the greenish cast should be corrected with white balance. Useful processing steps mentioned in the answers are:

• dehaze / haze removal
• increase local contrast
• add some sharpening
• set better black and white points with curves
• even out the sky brightness before contrast adjustments

One suggested method is to duplicate the image, blur it heavily so stars disappear, then use that blurred version to help flatten the sky gradient before doing curves and contrast work. A masked adjustment can also selectively darken areas away from the Milky Way if your goal is a more artistic result.

So: decent start, but the scene is fighting heavy light pollution. For a stronger result, focus on correcting the color cast, reducing the sky gradient, and boosting contrast carefully so the Milky Way stands out without making the image look unnatural.