Add touch-to-logical coordinate mapping for UI

Implements tapToLogical() to convert normalized touch coordinates to orientation-aware logical screen coordinates. Adds TouchRegistry hit testing for interactive UI elements and header back button. Touch gestures now work correctly across all screen orientations (Portrait, Landscape, etc.) by inverting the rotateCoordinates transform.

src/components/TouchRegistry.h

@@ -0,0 +1,53 @@
+#pragma once
+
+#include <array>
+#include <atomic>
+#include <cstddef>
+#include <cstdint>
+
+#include "components/themes/BaseTheme.h"  // Rect
+
+// Frame-scoped registry of tappable UI elements. Theme draw methods record each
+// interactive element's LOGICAL rect + id during render() (on the render task);
+// the input layer hit-tests a tap against it during the next loop() (main task).
+//
+// Lock-free single-writer (render) / single-reader (loop) via double buffering:
+// render writes the back buffer and publish() atomically flips it to live, so the
+// reader never observes a half-built frame. No per-frame heap allocation.
+//
+// Runtime-gated: disabled on boards without touch (setEnabled(gpio.hasTouch())),
+// so add()/hitTest() are a single branch on the C3.
+class TouchRegistry {
+ public:
+  enum Kind : uint8_t { Item = 0, Back = 1 };
+
+  static TouchRegistry& getInstance();
+
+  void setEnabled(bool enabled) { enabled_ = enabled; }
+  bool isEnabled() const { return enabled_; }
+
+  // Render task: clear the back buffer, append targets, then publish.
+  void beginFrame();
+  void add(const Rect& rect, int id, Kind kind);
+  void publish();
+
+  // Main/loop task: find the topmost target of `kind` containing the logical point.
+  // Returns true and writes its id to outId on a hit.
+  bool hitTest(int x, int y, Kind kind, int& outId) const;
+
+ private:
+  static constexpr size_t CAPACITY = 48;  // worst case excl. keyboard grid (Phase 2)
+
+  struct Target {
+    Rect rect;
+    int16_t id;
+    uint8_t kind;
+  };
+
+  uint8_t backIndex() const { return live_.load(std::memory_order_relaxed) ^ 1u; }
+
+  std::array<std::array<Target, CAPACITY>, 2> buffers_{};
+  std::array<size_t, 2> counts_{0, 0};
+  std::atomic<uint8_t> live_{0};
+  bool enabled_ = false;
+};