I prefer its as nickname for Katherine if used as first name. I love it it on its own as middle name. My name is Kaitlin and I plan to use Kate as a middle name for a future daughter to honor myself.
I have always liked Kate by itself, I find it simple yet spunky. It's actually a part of my first name (Jessica-Kate) but I don't really identify with it when it's not attached to Jessica. I also think it's nice as a nickname.
It's kind of bland and boring and feels 80s/90s because Kate, Katie, Caitlin, Katherine etc. were super common back then. It is much better as a nickname. Katerina nn Kate is nicer.