refactor(ui-core): move GPS trail sampling into TrailEngine

TrailStore, background sampling, auto-pause and the pre-shutdown
auto-save move from UITask to ui-core/TrailEngine.h. TrailScreen still
drives the store directly. The 512-point store now lives on the heap
with the rest of UiCore (static RAM -8 KB on Wio L1, same total).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

examples/companion_radio/ui-core/TrailEngine.h

@@ -0,0 +1,79 @@
+#pragma once
+// GPS trail: the RAM TrailStore plus its background sampling (runs while the
+// trail is active, independent of which screen is shown), auto-pause, and the
+// pre-shutdown auto-save. Recording control (start/stop/clear/save/load) is
+// still done by TrailScreen directly on the store.
+
+#include "../Trail.h"
+#include "../GeoUtils.h"
+#include "CourseEngine.h"
+
+class TrailEngine {
+public:
+  void begin(NodePrefs* prefs, const CourseEngine* course) { _prefs = prefs; _course = course; }
+
+  // Skips silently if no GPS fix; the min-delta gate inside addPoint() avoids
+  // near-stationary spam.
+  void loop() {
+    if (!_trail.isActive()) _pause_has_ref = false;   // fresh ref on next start
+    if (!_trail.isActive() || _prefs == NULL
+        || (int32_t)(millis() - _next_sample_ms) < 0) return;
+    _next_sample_ms = millis() + (uint32_t)TrailStore::SAMPLING_SECS * 1000UL;
+    int32_t la, lo;
+    if (!_course->currentLocation(la, lo)) return;
+    uint16_t md = TrailStore::minDeltaMeters(_prefs->trail_min_delta_idx, _prefs->units_imperial);
+    // Auto-pause: freeze the trail once the device has stayed within
+    // TRAIL_AUTOPAUSE_MOVE_M of one spot for the configured delay; resume on
+    // the next real move. Its own coarse gate (not the trail min-delta) so
+    // GPS jitter while parked doesn't keep the idle timer alive.
+    uint16_t ap = NodePrefs::trailAutoPauseSecs(_prefs->trail_autopause_idx);
+    if (ap > 0) {
+      uint32_t now = millis();
+      float moved = _pause_has_ref
+          ? geo::haversineKm(_pause_ref_lat, _pause_ref_lon, la, lo) * 1000.0f
+          : 1e9f;
+      if (!_pause_has_ref || moved >= (float)NodePrefs::TRAIL_AUTOPAUSE_MOVE_M) {
+        _pause_ref_lat = la; _pause_ref_lon = lo;
+        _pause_has_ref = true;
+        _last_move_ms  = now;
+        if (_trail.isPaused()) _trail.setPaused(false);
+      } else if (!_trail.isPaused() && (now - _last_move_ms) >= (uint32_t)ap * 1000UL) {
+        _trail.setPaused(true);
+      }
+    } else if (_trail.isPaused()) {
+      _trail.setPaused(false);   // feature turned off → resume
+    }
+    if (!_trail.isPaused())
+      _trail.addPoint(la, lo, (uint32_t)rtc_clock.getCurrentTime(), md);
+  }
+
+  // True while a trail is recording and not auto-paused (needs live GPS).
+  bool isRecording() const { return _trail.isActive() && !_trail.isPaused(); }
+
+  // Auto-save the live trail before power-off when the user enabled it
+  // (Tools › Trail › Settings › Auto-save). This covers the low-battery
+  // auto-shutdown, which otherwise loses the whole route. Overwrites /trail
+  // (same file as the manual Trail › Save); guarded on count()>0 so an empty
+  // trail can't wipe a previously saved one.
+  void onShutdown() {
+    if (!_prefs || !_prefs->trail_autosave_lowbatt || _trail.count() == 0) return;
+    DataStore* ds = the_mesh.getDataStore();
+    if (!ds) return;
+    File f = ds->openWrite("/trail");
+    if (f) { _trail.writeTo(f); f.close(); }
+  }
+
+  TrailStore& store() { return _trail; }
+
+private:
+  NodePrefs*          _prefs  = nullptr;
+  const CourseEngine* _course = nullptr;
+  TrailStore _trail;
+  uint32_t _next_sample_ms = 0;
+  // Auto-pause: _pause_ref is the last position the device was considered
+  // "at"; if it doesn't move beyond TRAIL_AUTOPAUSE_MOVE_M for the configured
+  // delay, the trail is auto-paused.
+  int32_t  _pause_ref_lat = 0, _pause_ref_lon = 0;
+  bool     _pause_has_ref = false;
+  uint32_t _last_move_ms = 0;
+};

examples/companion_radio/ui-core/UiCore.h

@@ -15,6 +15,7 @@
 #include "CourseEngine.h"
 #include "LiveShareEngine.h"
 #include "LocatorEngine.h"
+#include "TrailEngine.h"
 
 class UiCore {
 public:
@@ -24,6 +25,7 @@ public:
     course.begin(sensors);
     live_share.begin(prefs, &course, &events);
     locator.begin(prefs, &course, &live_share, &events);
+    trail.begin(prefs, &course);
   }
 
   // Driven from the frontend's loop(), before it drains `events`.
@@ -32,6 +34,7 @@ public:
     course.loop();
     live_share.loop();
     locator.loop();
+    trail.loop();
   }
 
   UiEventQueue events;      // Core → frontend; drained by the frontend's loop()
@@ -42,6 +45,7 @@ public:
   CourseEngine course;      // GPS position + course-over-ground ring
   LiveShareEngine live_share; // [LOC] auto-share session + peers' shared positions
   LocatorEngine locator;    // active target, geofence crossings, proximity beeper
+  TrailEngine  trail;       // GPS trail store, sampling, auto-pause, shutdown save
 
   // ── Models ────────────────────────────────────────────────────────────────
   MessageHistory history;   // channel + DM rings, delivery state, channel unread