backlog: add foresight live activity investigation

BACKLOG.md

@@ -144,6 +144,20 @@ Status: TODO / IN PROGRESS / DONE / BLOCKED.
   separate phase. Backlog ancestry: this was the original "relay could keep a
   rolling archive" idea — the archive is now P0 and the Trends graph (P1) is its
   visible half.
+- [ ] **Foresight Live Activity (heading-aware next station)** — investigate a
+  driving-time surface that predicts the likely next station ahead of the user
+  from cached data only (no extra source-data refresh on motion). Best v1 shape:
+  Live Activity option, not widget-first, because widget space/refresh budgets
+  are tight and the lock-screen/CarPlay compact slot better matches the use case.
+  Viable MVP: infer heading from recent motion/course, keep only stations in a
+  forward cone, score candidates by forward distance + lateral offset, and show
+  the next-ahead station with all three fuel prices or a compact rotating/focused
+  fuel treatment if space allows. Key caveat: heading is not full route awareness,
+  so avoid overpromising "the next station you will reach" on motorways/opposite
+  carriageways; frame as "next ahead" / "likely next stop" unless route-quality
+  heuristics improve. Must include hysteresis/speed thresholds to avoid flapping,
+  and should be tested specifically against compact Live Activity/CarPlay layouts
+  where space is extremely limited.
 - [ ] **Widget sparkline** — medium-widget mini sparkline of a favourite's 30-day
   trend, after the Trends UI lands (one-kind rule preserved).
 - [ ] **Price alerts for a specific station** — notify when a starred station's