It's less common now in the UK to admit people to PhD programs directly from undergrad. In many cases you'd be expected to do a one-year masters first, although that's not a universal requirement.

Nowhere near universal. It’s common to go from undergrad to PhD in the U.K.

Tbh most Master’s, esp MSc, don’t add anything.

Varies a lot from field to field.

>Don’t you normally need an undergrad to start a PhD in the US as well?

Yes, but not a graduate degree.

For comparison, at least in Austria, you need to have finished both a Bachelor of Science and a Master of Science in order to be able to start a PhD.

That's usually not the case in the USA (and some common law countries), where you only need the equivalent of a Bachelor of Science in order to start the PhD. You then do a small version of the Master of Science in parallel with the PhD.

So the UK is probably the best model - 3 years undergrad, 3-4 years PhD max.

Oh, that explains why I see more Americans going for PhD (successfully or not) than, say, Germans. It never made sense to me because I was used to it being the thing you can do after an MSc/MA and those already seemed like a questionable choice for many jobs.