polygon - Why the outcome of $area (geometry), is different from area saga shape indices tool in QGIS?

I am puzzled on why I get different outcomes on trying to calculate the area (m2) for multiple polygons in QGIS.

My polygons consist of tiny objects of few cm extent. When using $area (field calculator / geometry) for the smallest polygons I get 0.0000 while saga tool gives a value.

It seems saga shape indices area calculation is more robust, but is there a reason why $area (geometry) fails to produce an outcome and even in visually different polygons it gives similar values or even bigger values in smaller polygons?

The EPSG is set to 32631 31N (meters) so it shouldn't cause any trouble. I don't know what I am missing here.

$Area (as calculated by $area), area (add geometry column Project CRS), Area (saga shape indices tool)