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I think there is a misunderstanding about the baking process and the desired result.
Particle hair only works in Blender and is resource-hungry. you need to use a different technique for game engines.
One technique for game engines is to fake the required geometry with so-called hair cards. They are low-poly planes that use transparency and normal maps to ...
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Though you said you have done this, I still believe adjusting extrusion to something like ~0.02m would fix the issue (there is a clear projection of one leg on the other), and also check face orientations.
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As @Blunder mentioned, I just simply had to disable all of the hidden objects in renders as well! If it affects rendering, it affects baking.
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Have you tried to set up this way?
The image should be selected, but it doesn't mean that it should be connected in some way.
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Judging by how it looks and where it lines up, I'm fairly certain your normal map texture is not properly set as Non-Color. This must be set before you bake to it.
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Those dark lines indicate inconsistant normals.
You can find them easily with Overlay > Face Orientation: blue is forward, red is backward.
To fix those you can either select all polygons and recalculate normals or flip a selected area of normals manually with the flip normals command.
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