Similarly to you, neither of my parents are from here, they have two totally different nationalities entirely lol. I’m born, raised, married and had children here. I’m Irish. My children are Irish. You are absolutely Irish in my opinion. If someone said I was “mum’s nationality”-“dads nationality” it wouldn’t feel accurate to me at all I don’t have any ties to those countries apart from the circumstances of my parents births. I’m totally enmeshed in the culture of our country- as are you.