Grass paths are not affecting by smooth lighting as how grass and other blocks are, assumingly due to their different model. Also the path side texture doesn't look as nice as the grass side, as the grass was moved down by 1 pixel, but the shadow was not. I have attached an image of what the fixed texture could look like.
This is intended, see MC-64678 - as for the texture suggestion, please visit Minecraft Suggestions on Reddit or visit the Feedback website.
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