Hi Vojtech, you probably need to add a custom elevation source to your web scene.
If you're creating a 3D scene which is gong to show both - elevation above sea level (on land) and below sea level (or underwater - i.e. a river) you might need to have two elevation surfaces.
As far as I can see, the scene in the story map scene is using this:
Bathymetry: https://elevation3d.arcgis.com/arcgis/rest/services/WorldElevation3D/TopoBathy3D/ImageServer
DEM : https://elevation3d.arcgis.com/arcgis/rest/services/WorldElevation3D/Terrain3D/ImageServer
If you want a custom exaggeration applied to the bathymetry surface, you might need to have your own bathymetry surface (unless I missed something and you can now do some basic pixel calculations in a tile layer in AGOL; haven't done this in a while).
In the past, when I was creating web scenes that included underwater areas (i.e. river estuaries and seabed), i was creating a DEM from point bathymetry, then to exaggerate it I was simply using Raster Calculator in Spatial Analyst (i.e. cell value times 10: https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/raster-calculator.htm). Then I was publishing the resulting layer as a tile package with AGOL elevation scheme to my ArcGIS Online account and adding it to a 3D web scene as elevation source ( https://support.esri.com/en/technical-article/000014615#:~:text=Run%20the%20Share%20Package%20tool,a...
Also, I think you need to work with the local 3D scene in AGOL to achieve this. Hope you'll find something useful in the above notes.
