Here are two quick results using general-purpose image editors. In both cases, I first converted the JPG to a 32-bit per pixel working image.
In Affinity Photo, I used its HDR Tone Mapping, then applied Curves and Levels adjustments: In PhotoLine, I used its Optimize HDR adjustment, then Curves and Histogram adjustments: (In both programs, I used their capability of working in the Lab colour space for adjustment layers to adjust the Lightness (L) channel when adding the Curves adjustment.)
I also wanted to show the results of using a dedicated astrophotography program (FITS Liberator), but unfortunately the online JPG to FITS conversion utility doesn't seem to be working.
Note: Of course, your results will be much better since you can directly convert your 16-bit RAW photo to a 32-bit image without going through the ruinous JPG conversion....
