In my opinion this idea of 'living in the past' is just a way of saying 'thinking/talking about the past', I mean what else could it mean? You're not actually travelling in a time machine to the past to live, so, it can only mean thinking about/talking about the past. (Such a crime.)
I find myself thinking about the past a lot, trying to make sense of it, put it into a better perspective, or just thinking about times that were so real, full of emotions, and left an impression in my mind.
I equate this 'stop living in the past' idea to letting go. Letting go for good (if that's possible) or letting go in the moment in case you begin feeling too distressed.
I've heard of people having big letting go experiences which really transformed them, but for me it's about finding a perspective that allows me to let go of anger or hurt, and sometimes that just means to not think about it if I find myself starting to think about it. Self care.🙏