Export sRGB Material Color Values on FBX Export?

I want to bake the color values from high-resolution meshes to low-resolution meshes in Substance Painter. My High-Res Meshes have a specific color coding in their ID map.

When I want to bake the material colors they seem to be exported gamma corrected (as the HEX-Value suggests), so that they appear super dark in my bake. This color is supposed to be the exact color value from the Principled BSDF above.

Now the problem is that I cannot counter correct it in Substance, easily. Gamma correction changes the color value because it’s already clipped too low. Changing the whole color coding inside Blender also is out of the question as the colors need to be baked consistently in many files to come.

Is there a way I can disable gamma correction on the color values when exporting an FBX file from within Blender?

(edit) Or can the gamma correction be turned off somewhere?
I know this would brighten the color diaply in the viewport but it would at least export the correct values.

In hopes of someone being able to help me eventually:

I should specify the color terminology. Blender actually does export the color values without gamma correction.
I do want to export the color corrected values in sRGB, though. I’ve edited the title.

The problem being that I sometimes have to pick the color values from a list with the eye dropper. Blener is smart and color corrects the values automatically. When I export an FBX the values are saved without color management any more.

I do want the sRGB color corrected values attached to the FBX as color values on export.
Is that somehow possible?