To quote the PostGIS docs :
The basis for the PostGIS geometry type is a plane.
This is supported.
It also says
The basis for the PostGIS geography type is a sphere. The shortest path between two points on the sphere is a great circle arc. That means that calculations on geographies (areas, distances, lengths, intersections, etc) must be calculated on the sphere, using more complicated mathematics. For more accurate measurements, the calculations must take the actual spheroidal shape of the world into account.
To implement this, whoever requires it would need to add GeographyColumnMapping in pg2postgis and in jts2postgis (and its subclasses), and then add the requisite entries to the XXXDatastoreAdapter classes.
See https://www.postgis.net/workshops/postgis-intro/geography.html
To quote the PostGIS docs :
This is supported.
It also says
To implement this, whoever requires it would need to add
GeographyColumnMappingin pg2postgis and in jts2postgis (and its subclasses), and then add the requisite entries to theXXXDatastoreAdapterclasses.See https://www.postgis.net/workshops/postgis-intro/geography.html