You can make material with tone mapping.
I do not think if tone mapping for textures is dowable just in unreal (probably need gimp or photoshop)
You also can do tone mapping in post process material.
That color difference may be cause by how unreal calculates RGB values, while most of applications like photoshop have slightly different calculations. I just cannot remember term/keyword to google for it. It was topic here on forum about calculating color to HEX RRGGBBAA and back and what caused different colors.
ps.
I looked into plugin code, and it uses unchanged RGB values to create output. So if your input works like photoshop (or gimp) and scales RGB/ I remember keywords: its linear RGB and sRGB. So maybe you have different values as input. Like textures are sRGB while plugin expects linear RGB
I am not sure if that github has all code for plugin, but if it has, you can add lines converting RGB output.
another documentation about sRGB and linear RGB:
Edit i watched your video again, and yup it looks like one side is using sRGB while other is using linear RGB. Just not sure which is what.
pps.
there are multiple tutorials about tone mapping on yt. Gumroad will probably be about how to tonemap so your maps look better etc, and not about technical side of it.
last edit for now:
this whole mismatching of colors may be because one window (for what you paint) uses sRGB and other just RGB. So as result you see different colors, but both are correct RGB values. So creating material that corrects gamma and checking which one needs it may solve whole problem. As both areas (one you paint on, and another you see serialized) will have same RGB values and same gamma correction.