As said in the comments, circle is a native postgres type that is not related to postgis. If using PostGIS, it is better avoid these native types.
That being said, if you really have to use the circle type, you can convert it to a native polygon which in turn can be converted to a postgis geometry and then can be exported as a geojson:
select st_asGeoJson(CIRCLE(POINT(16.56115880637268,46.959564402028334), 4000)::polygon::geometry);
st_asgeojson
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{"type":"Polygon","coordinates":[[[-3983.438841194,46.959564402],[-3447.540456331,2046.959564402],[-1983.438841194,3511.06117954],[16.561158806,4046.959564402],[2016.561158806,3511.06117954],[3480.662773944,2046.959564402],[4016.561158806,46.959564402],[3480.662773944,-1953.040435598],[2016.561158806,-3417.142050736],[16.561158806,-3953.040435598],[-1983.438841194,-3417.142050736],[-3447.540456331,-1953.040435598],[-3983.438841194,46.959564402]]]}
(1 row)
PS: and of course this assumes that the radius is expressed in the same unit as the point coordinate, which seems unlikely with the given example.
If using a point in lat-long with a radius of 4000 meters, one way of doing it with PostGIS would be to cast to geography first:
select st_asGeoJson(St_Buffer(st_makePoint(16.56115880637268,46.959564402028334)::geography, 4000));
st_asgeojson
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
{"type":"Polygon","coordinates":[[[16.613712465,46.958835611],[16.612491754,46.951830285],[16.609299221,46.94512255],[16.604258179,46.938970016],[16.597562745,46.933608891],[16.58947033,46.929244935],[16.580291722,46.926045599],[16.57037918,46.924133621],[16.560112962,46.923582349],[16.549886822,46.924412934],[16.540092986,46.92659353],[16.531107204,46.9300405],[16.523274396,46.93462161],[16.516895464,46.940161074],[16.512215741,46.946446268],[16.509415535,46.953235867],[16.50860313,46.960269079],[16.509810522,46.967275657],[16.51299207,46.97398627],[16.518026136,46.98014287],[16.524719661,46.98550863],[16.532815529,46.989877084],[16.542002423,46.993080098],[16.551926824,46.994994372],[16.562206668,46.99554621],[16.572446128,46.994714373],[16.582250948,46.992530899],[16.591243707,46.989079863],[16.599078423,46.984494118],[16.605453903,46.978950156],[16.61012534,46.972661284],[16.612913687,46.965869389],[16.613712465,46.958835611]]]}
ST_BUFFERinstead – Ian Turton May 03 '22 at 07:50