Widget diagnostics: beacon from makeEntry (keychain + relay) + app diagnostics section

The small-widget skeleton survived four resolution fixes; instrument the
widget instead of guessing. Every makeEntry now writes its entry state
(intent type, location source, station count, fuel, sort, favourites flag,
first station) to a keychain beacon (app-readable) and fire-and-forgets a
GET to the relay's /api/v1/widget-diag so its access log records whether a
widget timeline actually runs in the extension and what it produced.
Settings → Debug gains a Widget Diagnostics section: the keychain beacon +
the installed-widget inventory from WidgetCenter. Relay gains the
/api/v1/widget-diag route (204, log-only).

FuelBoard/SettingsView.swift

@@ -45,6 +45,28 @@ struct SettingsView: View {
     @State private var debugMode: Bool = FuelStore.loadDebugMode()
     @State private var versionTapCount = 0
     @State private var lastVersionTap = Date.distantPast
+    /// Widget diagnostics: the extension's last makeEntry beacon (keychain)
+    /// + the installed-widget inventory from WidgetCenter.
+    @State private var widgetDiagBeacon: String?
+    @State private var installedWidgets: String = ""
+
+    private func refreshWidgetDiag() {
+        widgetDiagBeacon = FuelStore.loadWidgetDiag()
+        WidgetCenter.shared.getCurrentConfigurations { result in
+            let text: String
+            switch result {
+            case .success(let widgets):
+                text = widgets.isEmpty
+                    ? "No widgets installed"
+                    : widgets.map { "\($0.kind) · \($0.family)" }.joined(separator: "\n")
+            case .failure(let error):
+                text = "Error: \(error.localizedDescription)"
+            }
+            Task { @MainActor in
+                installedWidgets = text
+            }
+        }
+    }
 
     var body: some View {
         NavigationStack {
@@ -110,6 +132,32 @@ struct SettingsView: View {
                         Text("The first button applies the real criteria — cheapest \(alertsFuel.displayName.lowercased()) station within \(distanceUnit.format(alertsRadiusKM)) of you — and sends the actual station's name, price and coordinates. The second fires with no criteria at all (nearest seller), still carrying a real station, just to verify a notification appears and tapping it opens directions. Cheapest in range mirrors the app list (selected fuel + distance); the in-range count mirrors the alert radius.")
                     }
                     .onAppear { onRefreshDebugStatus() }
+
+                    Section {
+                        Button {
+                            refreshWidgetDiag()
+                        } label: {
+                            Label("Refresh widget diagnostics", systemImage: "arrow.clockwise")
+                        }
+                        if let widgetDiagBeacon {
+                            Text(widgetDiagBeacon)
+                                .font(.caption2)
+                                .foregroundStyle(.secondary)
+                                .textSelection(.enabled)
+                        } else {
+                            Text("No widget beacon yet — add a widget on the home screen, then refresh.")
+                                .font(.caption2)
+                                .foregroundStyle(.secondary)
+                        }
+                        Text(installedWidgets.isEmpty ? "No widgets installed" : installedWidgets)
+                            .font(.caption2)
+                            .foregroundStyle(.secondary)
+                    } header: {
+                        Text("Widget Diagnostics")
+                    } footer: {
+                        Text("The beacon is written by the widget extension at the end of every timeline entry (keychain, so it survives free-SideStore installs). Installed widgets come from WidgetCenter.")
+                    }
+                    .onAppear { refreshWidgetDiag() }
                 }
 
                 Section {