It would probably have been best to see your original image to see if some similar adjustments could be done without creating the halo. If you provide the same view of the original, forum members could probably provide additional suggestions.
As an another example of what can be done with the image you provided, I used the PS neural filter to reduce JPEG artifacts, followed by using Topzaz Phots AI for strong sharpending and the a PS Camera Raw filter where I added a bit of dehaze, clarity, texture, sharpening, and reduce the highlights a bit.
Of course I did this over the entire image to provide a shaper look over the whole image and not just the edges and they not be what you want.
Just some more ideas of what to consider.
Hope this helps some.