It looks like the feature is called Auto Shift in QMK/VIAL (I had to open up VIAL to remember the term).

I’m not sure I have a good answer for quick typing, I was in the process of implementing urob’s timeless homerow mods for ZMK when I fried my ZMK board. I know there are QMK implementations (maybe in userspace?), but my quick googling didn’t come up with what I was thinking.

Others have mentioned some of the boards on this list, but YAL should be pretty comprehensive list of boards with dpads

I thought it might fall into the non-split ortholinear category, but that makes sense once you pointed it out.

It only fulfills point 4 I think, but it does look like it might not be in line with the rules on the sidebar, so it will probably get removed (admittedly I don’t know if posts need to be manually approved here, so I’m not sure about this).

It might not be “hand-shaped”, but the use of layers (and tap-dance/home-row mods) will minimize hand-movement, which is another way to approach ergonomics.