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