I can reproduce the behaviour with AutoCAD 2024.
The two regions in the DWG are valid. But if I _UNITE them, the resulting region looks OK, but it doesn't show geometry properties like area and circumference.
If I use the command SNOOPENTS from ArxDbg.arx (<ARX>\samples\database\ARXDBG) I get the error messages
ERROR calling AcDbRegion::getAreaProp()
ARX ERROR: eInvalidInput
Also the AutoCAD command _AREA _OBJECT can't calculate the area.
The AutoCAD command _MASSPROP however displays values for area (Fläche) and circumference (Umfang):

The geometry of one region is very complex. It has a lot of "touching points" that makes it hard to decide whether there is one region with a hole or multiple separate regions. I suppose that this causes the problem.

Looks like a bug. So I think this is a case for the AutoCAD product support.
I managed to create a valid united region like this:
- _EXPLODE all regions to lines
- Create new regions with _REGION and select all lines.
- Unite all new regions with _UNITE
See attached DWG. I think you can do the same programmatically with ObjectARX. This could be a workaround for you.
Thomas Brammer ● Software Developer ● imos AG ● LinkedIn ● 
If an answer solves your problem please [ACCEPT SOLUTION]. Otherwise explain why not.