you already said you were on a bigger bike before
I am old and not very flexible and I'm your exact height. That is an older bike and definitely racy geometry. If you looked at new Trek Domane or Spec. Roubaix there'd be way more headtube and therefore the bars would be higher. And then you could go higher with a higher stem angle too. It's not how you look on the bike, it's how you feel. I bet if you get some modern bars that enable better shifter placement and raise the height of the bars then you won't have to crane your neck to see the road. In other words a more upright riding position.