Yes, I tried what you suggested and it does solve the visibility.
For prosperity I have described what I found below.
I hope I understand this function correctly now.
For a wall that is visible on home storey only & symbolic cut floor plan display:
1) It seems the doors set to projected automatically takes the symbolic cut property of the wall.
1.1) changing Opening lines 3D projection deg does not have any influence.
For a wall that is visible on home storey only & projected floor plan display:
2) It seems the doors set to symbolic does NOT automatically take the projected property.
2.1) changing Opening lines 3D projection deg now does change the door swing on plan, if the doors are set to projected.
For a wall that is visible on all relevant storeys:
3) The symbolic cut option is greyed out.
3.1) So doors have to be manually set to "symbolic cut"
ArchiCAD24 - since Nov 2020
Revit - 2005 to 2020
Windows 10 Pro
2 screens: nvidia quadro RTX 4000