Gel nail polish

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

Yes.
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.

What about the rema in סימן קצח סעיף א
הגה ולכתחלה לא תטבול אפילו בדברים שאינן חוצצין גזרה אטו דברים החוצצין.

The Rabbi didn’t Pasken like that Rama

If a woman forgot to cut one of her nails is the tevilah invalid?
Is there a difference between the hands and feet being that she is not makpid regarding toe nails

Food stuck in teeth does that make the tevilah invalid

Thank you
all Jews from askanazic descent follow this rema being that all the commentators on shulchun aruch including the ש״ך ט״ז פתחי תשובה all go with this rema,
All the leading poskim in the ashkenazic world of halacha follow this rema , to clarify is this psak limited to sefardim or ashkenazim as well ?

Something i learned a long time ago. There’s no such the as “all leading poskim” or “everyone holds”. Maybe we can expound after YT.

Regarding your question, this is Rav Abadi’s Psak for all.