There doesn’t appear to be a car detailing tag, only car repair and similar.
AFAIK it is one of cases where we have no tagging schema yet
something needs to be invented - and I have no idea should it be new top level tag, subtag of existing or what
situation says something about biases of OSM community
shop=car_detail is used 65 times but no idea is it a good tag name or should different be invented (not documented, low use - currently whoever documents tag for that has decent chance to choose tagging for it)
When Google Maps is their operation - a reserved corner of the shopping centre carpark, together with a storage locker, would we still call it a “shop”?
If I understand car detailing correctly, it is high-end valeting and stuff like polishing, ceramic coating etc? Maybe craft=car_valet[ing] or =car_detailing. Do they not come to where you are anyway? If so, difficult to map unless they also have a unit somewhere.
There are 375 service:vehicle:detailing | Keys | OpenStreetMap Taginfo.
Mostly in combination with shop=car_repair, and a few on amenity=car_wash.