It’s still common practice. The general idea is not to shove your watch in people’s faces, but have it hide under your cuff as long as you don’t look at it.

I have the same issue as you. Most cuffs make it hard to wear it like that. I can do it with a diver but it doesn’t automatically slide under. I have to help it a bit. I got only one super slim quartz watch that makes “under the cuff” effortlessly with my wrists. Custom shirts would help but watches are already expensive enough. 😀

Maybe find a brand of shirts with bigger cuffs. Some online tailors (if you want to go that route) offer to adjust the left cuff to allow for room for a watch.

Or simply just go with the flow of all the people that wear a 55mm Garmin apocalypse watch with a dress shirt nowadays.

Omega speedmaster x-33 springs to mind. There were also speedmasters with the appearance of a round Casio a168.

And nowadays a couple of luxury watch labels came out with smart watches, which fit your question as they don’t have touch screens or smart watch appearance, but they also don’t fit your question as there is nothing obviously digital about them. Frédérique Constante and Alpine have something: https://www.luxuriousmagazine.com/frederique-constant-and-alpina-announce-the-swiss-horological-smartwatch/

Also Google the Seiko Arnie and you’ll find an old digital dive watch from some Schwarzenegger movie, which has quite a connaisseur pricing these days, so it might qualify for luxury (or not)