There are hundreth of Barometer Apps out on Play.
Which one is without Ads, free and uses the least permissions?
(Or How could I find out this myself without looking at each detail page in Play?)
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For alternatives, you might wish to take a look at my app lists. At a glance you can see here rating (ordered by that, decending, so the best rated apps come first), price, number of permissions, and more – right from the list, so no need to call up "detail pages". You can even search apps by permission, i.e. list apps for given categories which do (not) have specific permissions you name (see also: How to search the Play Store by permissions? on Android.SE).
I would suggest Barometer Reborn
It has only location permission for My Places functionality. If you don't use My Places functionality then it does not fetch location.
More info about the app at https://www.barometer-reborn.com/