All/most of the new stations on the Elizabeth line are going to have barriers afaik. It seems to me like all the new/refitted underground stations are getting the barriers these days too - I think it's a great improvement personally.
How about making a study, counting all metro stations noting whether they have platform screen doors, automation, and the year built. You'll very likely see there's a strong connection between automation and platform screen doors, but less so for the other variables.