Nominatim is reporting these objects as zipcode 94134:
https://www.openstreetmap.org/way/274668291
https://www.openstreetmap.org/way/103383625
https://www.openstreetmap.org/way/290557232
https://www.openstreetmap.org/way/290559578
https://www.openstreetmap.org/way/289935112
https://www.openstreetmap.org/way/195467121
https://www.openstreetmap.org/node/4951863007

Since there are no objects nearby with 94110 it will report 94134.  So to "fix" nominatim, something close to this point needs to be correctly marked with 94110.  Is the whole "bernal heights" https://www.openstreetmap.org/way/635461859 94110?