> Or is it my mistake and "luxury shop" would be treated as shop category in UK

In a sense it is a shop category, but it's not a very useful one for OSM, because OSM tends to concentrate on "vertical" categories (what is sold, regardless of price) rather than "horizontal" ones (like this is) - although https://taginfo.openstreetmap.org/tags/shop=variety_store is another example of the latter.
The industry does have specialists in the former - https://en.wikipedia.org/wiki/LVMH is an obvious one.
Some of the examples here do have lots of other examples - play around with https://overpass-turbo.eu/s/1tOg to see the sort of tags used for edge cases and you'll see only one other "yes" - mappers do tend to have a go at classifying these to sensible values (even if they can't always agree on what).
There was one advertised data consumer for these (me): https://taginfo.openstreetmap.org/tags/shop=luxury#projects .  They were included in a category less general than yes: https://github.com/SomeoneElseOSM/SomeoneElse-style/blob/master/style.lua#L7697 .
