feat(player): add mobile directional pad controls

MVP.md

@@ -228,9 +228,11 @@ Browser controls must support:
 - The player map consumes all space not required by fixed status and control
   panels. The player view supports a minimum `412 x 916` CSS-pixel viewport
   without page scrolling.
-- Computers support keyboard movement and on-screen arcade controls. Tablets
-  support swipes and on-screen controls. Phones use directional swipes without
-  on-screen directional buttons.
+- Computers and tablets support keyboard, swipes, and on-screen arcade
+  controls. Phones show an always-visible four-button directional pad as the
+  primary touch control while retaining avatar drag and directional swipes as
+  optional alternatives. The pad sends only existing orthogonal movement
+  intentions through the authoritative server path.
 - An always-visible `OK` control with a key icon drops the carried key without
   confirmation and exposes the Russian accessible label `Сбросить ключ`.
 - Observer mode requires at least a `1024 x 768` CSS-pixel viewport, initially