I fear you are getting this wrong. If you want a sharp “pixel art”-look its mainly about how your game reads and interprets that texture. You can paint it in blender if you want, just use change the interpolation method in the shader that blender uses to “closest” as it has been mentioned and use a lowes texture, eg 32x32 pixels or whatever you have in mind. Changing the setting in the nodeeditor doesnt make the texture being stored differently, its just about how its read/displayed in blender while you create it / paint it. At the end its just that your target game that has to interpret the texture the same way. So if that third party game interprets all its used textures like that aswell then you are already done. You very likely wont be able to change it in the game engine if I got your usecase right, so you have to upscale the image from your lowres (32x32) to a higher (eg 1024x1024) res with an image editor of your choice and prevent unwanted filtering in that step. Pretty much any imageeditor has a filtermethod you can choose for scale, so set it to filtermethod “none”, like I did in the example posted.
Example:
