All Sony needs to do is take the PS Portal, update it's hardware and add a 4 core, 12cu APU and make that the PS6 controller included in the box. Keep the spec low so the PS6 overall price would be bellow the PS5 Pro.
This would add a whole new experience to PS6 games by having two screens. The TV screen is clear of any UI clutter and the controller locally renders the map, inventory, chat, hub, etc.
When playing away from the TV, the controller switches to Stream Mode via Wi-Fi 7 (direct) or 5G.
Or
Local Render Mode for all PS4 and select PS5 games.
That's it, no reason to do two products (handheld and console) or a complicated design.