Praise be to Allah.
If the nail polish – whatever it is called or however it is manufactured – is simply a dye or colour, with no substance, in the sense that it does not form a separate layer over the nail, then this does not prevent water reaching the nails, hence wudoo’ is valid if done whilst wearing it and it does not have to be removed.
But if it forms a layer that prevents water from reaching the nails, then it must be removed before doing wudoo’, because one of the conditions of wudoo’ being valid is that the water must reach all of the part of the body that is being washed and must touch it directly with no barrier in between.
We are not entirely sure about the components of the nail polish mentioned in the question or the way in which it is used, and we do not know how it works or how the company that makes it explains how the water reaches the nail, or whether what passes through is water or just moisture. We are very doubtful as to whether this nail polish actually allows water to reach the nails.
If it is only moisture, that is not sufficient for wudoo’ to be valid, because one of the conditions of the validity of washing any part of the body in wudoo’ is that water should be able to flow over it, and it cannot be merely wiped with something damp. It is not permissible to deliberately omit even the smallest part of the limb and not let water reach it, because of the report narrated by Abu Dawood with a saheeh isnaad from some of the companions of the Prophet (blessings and peace of Allah be upon him), according to which the Prophet (blessings and peace of Allah be upon him) saw a man praying, and on the top of his foot there was a spot the size of a dirham that had not been touched by water. Hence the Prophet (blessings and peace of Allah be upon him) instructed him to repeat his wudoo’ and his prayer.
Because we have not come across this substance ourselves and we cannot find anyone who has tried it or seen it, it suffices us to mention the shar‘i principal referred to above, and we will leave the practical details to specialists who deal with such matters, because they are more able to identify what exactly this nail polish is and what its nature is, so you should ask trustworthy people who have the appropriate expertise and are religiously committed.
Even if we assume that this type of nail polish allows water to pass through, calling it “Islamic nail polish” does not make it permissible for a woman to go out wearing it, because it comes under the heading of adornment that it is not permissible to show in front of non-mahram men.
And Allah knows best.