In reply to restless native:
Top tip: carry ID if you don't want to parch.
I was in Kleinwalsertal, yesterday, and had to trudge back to the car to fetch mine because, despite having my vaccination certificate on me, the watering hole wouldn't let me in without ID along with it -- if the plod comes along to have a look-see, apparently, they'll be wanting to see vaccination certificates WITH ID.
I never carry ID on the hill and, for some reason, I still didn't, yesterday, even though I *did* remember my vaccine certificate. I'd even printed that on actual paper because my phone is another thing I don't generally carry on the hill -- phone and wallet generally live in my car unless I'm going up something extreme or on my own.