Welcome to OpenStreetMap and thanks for adding the building.

The ref tag on a post box refers to its unique reference number. If you wish to add its postcode, you can use the postal_code tag.

The addr:postcode is only used for addressable features on the map, which you correctly used for the building you added. For things like post boxes, postal_code is used.

I've restores the ref in
https://www.openstreetmap.org/changeset/163189209

See also:
https://wiki.openstreetmap.org/wiki/Tag:amenity%3Dpost_box
https://osm.mathmos.net/postboxes/