Zone numbers refer to the German definition?

Yes, this is right for GK.

So how should I change the east component to conform to JAG3D format?

I'm not sure because I'm not familiar with M28 and its definition. However, these settings relate to the reduction of the horizontal distance, and the projection is not related to the adjustment problem. This task is usually done by the total station during the field work (or can be done by hand using Excel or some tools like that).

So, my recommendation is - in general - to prepare the distances w.r.t. to your projection and afterwards import the corrected horizontal distances in JAG3D instead of the raw data. Please find below the method implemented in JAG3D. Please check it, if it works for your modification.

     double m0 = reductions.getProjectionType() == ProjectionType.UTM ? 0.9996 : 1.0;
     double yS = this.getStartPoint().getY();
     double yE = this.getEndPoint().getY();
 
     // Reduce east coordinate
     yS = ((yS/1000000.0)%1)*1000000.0-500000.0;
     yE = ((yE/1000000.0)%1)*1000000.0-500000.0;
 
     double k = (yS*yS + yS*yE + yE*yE)/6.0/R/R;
     obsDist = m0 * (1.0 + k) * obsDist;

Kind regards
Micha

I have GK coordinates M28 with
Meridian: E10° 20′
East Components are negative.

Trying to run the adjustment gives me
Projection cannot be applied to observations because the coordinates are invalid, e.g. missing zone number!

Zone numbers refer to the German definition?

So how should I change the east component to conform to JAG3D format?
-57500.000

My current approach:
-57500.000 + 500000 with 3 as prefix => 3442500

Thanks!