Reading her post, I assume the OP wants the opposite: her soft brushes result in a hard edge, which is not supposed to happen.
- Change your Color settings: Edit-->Color Settings, and check Blend RGB Colors Using Gamma 1.00
- Change your image bitdepth to 16bpc. Image-->Mode--->16bits per channel.
- load up the basic brushes brush set, and use those.
Avoid painting in 8bit mode in Photoshop - it doesn't work that well. Very noisy blending in the edges.
Photoshop doesn't allow the user to control the softness curve, and create a custom transfer curve for the edge blending. Resulting in less than ideal edge blending in cases. Krita allows for a custom softness curve.
PS I stopped drawing and painting in Photoshop years ago. I now use Krita and ClipStudio instead.
I 100% agree with Rayek's advice on using a 16 bit workflow.
However, I would not normally check "Blend RGB colours using gamma 1" when working in 8/16 bit color depth and the normal Adobe/sRGB color spaces. This can lead to several other negative effects e.g. Photoshop will only do normal blending mode in the gamma specified and a 8 bit workflow in particular does not have the precision needed to work in gamma 1.0.
There are a few other things to check though.
Is the harsh edge only visible against the transparency checkered background?. There is a display artefact in Photoshop which shows banding and hard edges against that transparency background. It is not present in the resulting image though. You can easily check by putting a temporary solid layer at the bottom of the layer stack (say solid grey or white). If the harsh banding disappears then you are seeing that artefact.
The second - if your brushes are acting abnormally, just to be sure, try resetting the brush tool
Thank you so much for your thorough help! I reset my brushes, but I think you're right about the transparency issue. I don't think I noticed it was the issue because on dark backgrounds, like dark blue and black, the soft brushes left a hard edge.