As far as the nail polish question in the OP, I haven’t tried for decades. I work in a field where the norm is a healthy look, business casual range of clothes, minimal makeup and no nail polish. So my thought is that the number one thing is to get the cracked dry skin under control. Do you actually have a form of dermatitis or eczema and might a doctor or dermatologist have suggestions? Most people don’t get cracked hands evrn in Canadian winters.
I would address that before I thought about nail polish. If your hands are chapped or cracked or raw, nail polish will draw attention to that and can also be an irritant. On the other hand, if your hands have healthy skin, short clean unpolished nails will look fine in most situations.
I’ve never found a nail polish that doesn’t chip off fairly quickly. I think the new gel nail polishes might require UV light to set? There has been a lot of innovation since I gave up on nail polish, I’ve never had fake salon nails or evrn been tempted.
My nails are however a bit bendy. So nail polish chips because the tips bend. Then the tip will just spontaneously crack off. The only time my nails grew nicely at all was when I was on more or less bed rest a few years back for a medical reason.