I think I need to provide some better photos, as they're obviously not clear.
This is a cavity wall in a 1960s bungalow that I'm renovating. There was previously a floating timber floor mounted on a concrete slab. I removed this floor and had the insulated screed floor installed on top of the concrete slab. The wall construction is brick outer leaf, 60mm cavity, block inner leaf, then my screed flooring.
The door is mounted directly inline with the outer leaf, but on top of a DPM, some small blocks of wood and then expanding foam infill. The doors do not straddle the cavity in any way. The cavity - which is 60mm wide - has been left entirely open.
I'm not sure what you mean about the floor matching what the walls are doing with respect to the cavity. The floor is level with the top of the inner leaf. The outer leaf finishes at around the same height, and the door/wood/foam is then sat on top of this.
I have no idea what's required from window and door installation. From my POV, the installer should've at least offered to close the cavity. He quoted me 3-4 days for installation, and did all the windows and doors in a day. So, it was rushed, and I've been left with issues like this as a result. A cavity closer should've been installed prior to the doors going in. But, now, I can't do that unless I find a retrofit cavity closer.