Gel nail polish

Can a woman go to the Mikveh with nails that are painted with gel & they are brand new?

But your question is very well stated.
In so far as they fresh, not cracked, chipped or other form of imperfection. Because if they are then they are in fact considered a chatzizah.

Just to clarify, when we say “brand new” or “fresh” is this a measure of time or just looking at them and they still look “brand new” or “fresh”?

Not a measure of time. They just can’t be cracked, chipped, or have any other imperfection.