You probably can while using Special K. Since the game doesn't have it's own in-game toggle, Kaldaien threw together a way to spoof a lack of HDR support in the game. This allows Special K users to then use Special K's retrofit HDR, which seems to result in a better HDR experience.
That probably had to do with AMD FidelityFX CAS available in the MS Store version -- that's a sharpening effect after all that sharpens textures and the like. If that feature was enabled during the comparison, the textures of the MS Store version would appear sharper in comparison to the Steam version.
Probably got interested enough in the game from seeing my various comments about it and examples of how the built-in HDR implementation felt lackluster.
You can -- Special K injected through the global injector stores its injected textures in the Documents folder -- within the profile folder of the game.
Just open Special K's control panel, hit File > Initialize texture mods, and then click on File > Browse Texture Assets > Injectable Textures to open the texture folder that modded textures should be put into.
As long as the textures haven't been changed, they should work fine in this version as well.
Here's GPUnity's NieR: Automata texture pack injected into the Microsoft Store version.
For comparison: