My observations would confirm that size is important.
Small birds, like sparrows, almost always hop.
Large birds almost always walk.
Those in between (blackbirds, crows) may use either or both.
Starlings are the smallest bird I know of that use walking almost exclusively.
I don't entirely believe your explanation, however. The birds that use both modes do not seem to pay that much attention to the roughness of the terrain. They'll use both modes over quite flat terrain. Crows seem to use hopping for speed - instead of running (although they more often walk than hop). Blackbirds on the other hand do run and rarely, if ever, walk (although they mostly hop).
I'd agree that the energy cost of hopping increases more quickly with mass. I can see another difference, too - in predator avoidance strategies. Running is better for getting under cover (blackbirds run, crouched down, when threatened - or they fly). Hopping is easier to turn into a takeoff.
Nudging and winking in that sense are probably quite old. Saying - or writing - the words instead of performing the actions may be quite old, too. It might have been done in a cartoon or a music hall performance. So I donâ€™t have any difficulty in imagining that it predated Python. But I have no idea when it started.
“Liquid Retina” is LCD technology. Apple only have it on the (less expensive) iPhone XR - the others iPhone X versions are all OLED. OLED displays are easier to find- most high-end Smartphones and even the mid-range use OLED displays. If OLED works for you it shouldn’t be too hard to find an Android phone which suits.