feat(player): add mobile directional pad controls

docs/UI_STYLE.md

@@ -64,7 +64,10 @@ are not MVP requirements.
 - Visible keyboard-focus outlines are not required for the MVP.
 - On computers, movement works from the keyboard and from an on-screen
   directional control cluster fixed in the lower-right corner.
-- On touch devices, the centered player avatar is the movement handle. Its
+- On touch devices, an always-visible four-button directional pad in the lower
+  right is the primary movement control. Its centre is inactive, each button
+  is at least 48 by 48 CSS pixels, and it sends only one cardinal intention.
+  The centered player avatar remains an optional movement handle. Its
   transparent touch target is at least 96 by 96 CSS pixels and its visible
   character remains unobscured. During a drag, it deflects no more than 28 CSS
   pixels from center and returns exactly to center on release, cancellation,
@@ -72,8 +75,9 @@ are not MVP requirements.
 - The avatar drag has a 12 CSS-pixel dead zone and directional hysteresis. Its
   bounded repeat cadence changes monotonically from 360 ms at a small
   intentional displacement to 170 ms at the target edge; it never exceeds the
-  server's 150 ms movement cooldown. Touch swipes remain supported. Phones do
-  not show a directional-button cluster.
+  server's 150 ms movement cooldown. The pad's hold repeat is 170 ms. Touch
+  swipes remain supported. The pad, avatar drag, swipe, and keyboard inputs
+  share one bounded latest-intent path.
 - The always-visible key-drop control is labelled `OK`, includes a key icon,
   and is positioned closer to the upper edge of the screen than the
   directional controls. Dropping does not require confirmation.