Stop Approx. distances beside routed values; add Best Value alert mode

Distances (the "Approx. 1.5 mi" report):
- Refuse junk CoreLocation fixes (invalid accuracy, or a coarse >300 m fix
  within 3 km of the position already held; a coarse fix in another city is
  real travel and is still accepted).
- Resolve ONE display basis per render through FuelStore.distanceDisplayOrigin,
  used by rows, radius filter, sorting, savings figures and the Live Activity,
  so a stray fix can no longer re-base the list outside the route cache's 600 m
  ring while the routed values sit unused in the cache.
- Treat an incomplete route set as a state: retry it after 30 s rather than the
  full 10-minute throttle, and repair a stale incomplete flag once every
  in-radius station has a route (nothing left to route, flag stuck down).
- Widget extension resolves the same origin for fetch, radius, ordering and
  labels, and keeps its own fix in fuelboard.widgetLocation instead of
  overwriting the app's GPS fix.

Alerts:
- Best Value as a distinct alert mode on the existing geofence/notification
  pipeline, with a persisted threshold; reverts to cheapest when the feature is
  unconfigured and is not selectable while disabled.

Diagnostics (DEBUG, gated): FB_DIST_FOCUS now prints FB-DIST-ORIGIN (candidate,
accuracy, anchor, offset, resolved branch, served origin), FB_FAKE_FIX feeds a
synthetic fix through the real guard, FB_STALE_INCOMPLETE forces the stale-flag
state, and the route-fill status is surfaced in Settings behind debug mode.

FuelBoard/AlertsView.swift

@@ -12,6 +12,9 @@ struct AlertsView: View {
     @Binding var enabled: Bool
     @Binding var radius: Double   // stored in km (monitor + storage)
     @Binding var fuel: FuelType   // the fuel alerts monitor for
+    @Binding var alertMode: AlertMode
+    @Binding var bestValueThresholdGBP: Double
+    let bestValueConfigured: Bool
     @Binding var favouriteDropEnabled: Bool
     @Binding var favouriteDropFuel: FuelType
     /// Whether alerts mirror the Stations-tab search distance (capped at 8 mi).
@@ -150,6 +153,16 @@ struct AlertsView: View {
 
                 Section {
                     Toggle(String(localized: "Cheapest station", comment: "Proximity alert toggle"), isOn: $enabled)
+                    Picker(String(localized: "Alert type", comment: "Proximity alert type picker title"), selection: $alertMode) {
+                        ForEach(AlertMode.allCases.filter { mode in mode != .bestValue || bestValueConfigured }) { mode in
+                            Text(mode.displayName).tag(mode)
+                        }
+                    }
+                    if !bestValueConfigured {
+                        Text(String(localized: "Set up Best Value first so Best Value alerts can account for your fill size, MPG and travel cost.", comment: "Best Value alert unavailable hint"))
+                            .font(.caption)
+                            .foregroundStyle(.secondary)
+                    }
                     Picker(String(localized: "Fuel", comment: "Fuel picker title"), selection: $fuel) {
                         ForEach(FuelType.allCases) { fuel in
                             Text(fuel.displayName).tag(fuel)
@@ -164,6 +177,18 @@ struct AlertsView: View {
                     Text(alertRadiusGuidance)
                         .font(.caption)
                         .foregroundStyle(.secondary)
+                    if alertMode == .bestValue {
+                        Picker(String(localized: "Minimum saving", comment: "Best Value alert threshold picker title"), selection: $bestValueThresholdGBP) {
+                            ForEach(FuelStore.bestValueAlertThresholdOptionsGBP, id: \.self) { value in
+                                Text(FuelSavingsFormat.money(value)).tag(value)
+                            }
+                        }
+                        if !bestValueConfigured {
+                            Text(String(localized: "Set up Best Value first so FuelBoard can account for your fill size, MPG and travel cost.", comment: "Best Value alert setup hint"))
+                                .font(.caption)
+                                .foregroundStyle(.secondary)
+                        }
+                    }
                     if enabled && monitoredCount == 0 {
                         Text(String(localized: "No stations monitored yet — open the Stations tab to load prices first.", comment: "No monitored stations hint"))
                             .font(.caption)
@@ -172,7 +197,10 @@ struct AlertsView: View {
                 } header: {
                     Text(String(localized: "Proximity alerts", comment: "Proximity alerts section title"))
                 } footer: {
-                    Text(String(format: String(localized: "When you approach a station that is the cheapest within the radius, FuelBoard sends a notification — even with the app closed. Nearby stations selling %@ are watched — favourites get priority — and each station alerts at most once per hour. Follow search mirrors the Stations-tab distance, capped at 8 miles for reliable geofencing. Smaller radii ping more often but later; larger radii ping rarely in town but earlier from afar.", comment: "Proximity alerts section footer"), fuel.displayName.lowercased()))
+                    let modeDescription = alertMode == .bestValue
+                        ? String(format: String(localized: "When you approach the Best Value station within the radius, FuelBoard sends a notification if it could leave you at least %@ better off after extra return travel. Nearby stations selling %@ are watched — favourites get priority — and each station alerts at most once per hour.", comment: "Best Value proximity alerts section footer"), FuelSavingsFormat.money(bestValueThresholdGBP), fuel.displayName.lowercased())
+                        : String(format: String(localized: "When you approach a station that is the cheapest within the radius, FuelBoard sends a notification — even with the app closed. Nearby stations selling %@ are watched — favourites get priority — and each station alerts at most once per hour. Follow search mirrors the Stations-tab distance, capped at 8 miles for reliable geofencing. Smaller radii ping more often but later; larger radii ping rarely in town but earlier from afar.", comment: "Proximity alerts section footer"), fuel.displayName.lowercased())
+                    Text(modeDescription)
                 }
 
                 if enabled, let lastAlert {