ST_Within does not return true

Solution 1:

EPSG:2193 has coordinates in metres so it is unlikely that your values (174.82726, -41.16671) are in that projection, it is much more likely that they are in degrees (WGS84, EPGS:4326). So you need to transform your point to compare them to polygons in EPSG:2193, thus your SQL should be something like:

select sa22018_v1_name from sa2_2020 where ST_Within(ST_TRANSFORM(ST_MakePoint(174.82726, -41.16671), 2193), geom);

ST_SetSRID only changes the metadata of the point (setting the CRS), to actually change the values of a point's coordinates you need to reproject the point (transform it from one projection to another) and so must use ST_Transform.