I want to align the diagonal beam so that the top right part is connected the same way as the bottom left part (as shown in the left picture below), so there is still a bit of the diagonal beam connected to the vertical one. I've tried lots of different things to get it connected the way i want, but with the snapping tool I only manage to get one side properly connected, on the other side it always snaps to the wrong vertex. In the past I did estimate what looked kind of nice, but for a project I'm currently working on it needs to be spot on. Is there any way to do this properly?
To have proper topology and avoid overlapping faces, create a loop cut on the two columns, one cut on the bottom of the left column, and one and a cut on the top of the right column.
Then select the newly created faces on the inside and do Bridge Edge Loops to join them with new faces. (the shortcut is Ctrl+E and select bridge edge loops)