James Derrick
Hi GinaroZ,
Looking at the website (logo cross-checked with Mapillary images), the options seem to be amenity=clinic or hospital.
Their formal regulatory registration (Not CQC - Scotland!), lists the site is a "private psychiatric hospital" and does include 7x24 emergency care.
https://www.healthcareimprovementscotland.org/our_work/inspecting_and_regulating_care/independent_healthcare/hospitals/castle_craig_hospital.aspx

The OSM wiki seems to have more detail on physical emergency care rather than mental health provision, but amenity=clinic is clear in that it excludes in-patients which points back to hospital.
I've therefore tagged:

amenity=hospital
healthcare=rehabilitation
healthcare:speciality=psychiatry


https://castlecraig.co.uk/about/history/castle-craig-hospital-peeblesshire-uk

Hope that makes sense!
Happy Mapping,

James