I used GP4000 and later GP4000s-II for years. I used them in 23mm, 25mm, and later 28mm sizes. The 28mm tires measured 31mm on my bike, and barely cleared the chainstays. GP4000sII tires have been great though, and I could continue using them happily.

However, when I wore out my most recent set I went to GP5000 tires instead. I got them in the 28mm size and was pleased to discover they do run truer to size. They measure 27-28mm on my wheelset (Fulcrum Racing Quattro 4).

Any evidence about flats / puncture resistance would be anecdotal at best. But for me, I've only had one flat with my GP5000s in about a thousand miles. On the other hand I seemed to average one flat every 300-400 miles on my GP4000sII tires. I'm a sample size of one, so it's not really a good metric. But they do seem pretty reliable to me. I doubt that I could judge accurately whether they roll better than the GP4000sII. Data on websites says they do. But again despite me being a sample size of one, and despite the confirmation bias implicit in wanting to like the thing you spent money on, I am happy with them, and find them to handle very well.

So I do consider them to be a great replacement for, and even upgrade to the GP4000sII. I'm happy to run them on my road bike.
(On my hybrid/commuter I'm pretty happy with GP4Season 32mm tires)