feat(lotw): show last sync time on settings, precise incremental cursor

The stored sync cursor was 'yyyyMMdd', which LoTW's qso_qslsince silently
ignores (measured live: it falls back to the system-supplied default).
Write a full UTC 'yyyy-MM-dd HH:mm:ss' cursor instead — the documented
format LoTW honors — so incremental pulls are exact (second precision)
and the settings page can show the last successful sync time on the LoTW
card, formatted like the ephemeris update time (prefs_updated_title).
Legacy yyyyMMdd cursors are normalized for the API, the gate and the
display (lotwCursorApi/lotwCursorDate/lotwCursorEpochMs).

feature/settings/src/main/java/com/rtbishop/look4sat/feature/settings/SettingsScreen.kt

@@ -338,6 +338,7 @@ private fun SettingsScreen(uiState: SettingsState, onAction: (SettingsAction) ->
                 LoTWCard(
                     settings = uiState.lotwSettings,
                     workedGridsCount = uiState.workedGridsCount,
+                    lastSyncEpochMs = uiState.lotwLastSyncEpochMs,
                     showLoTWDialog = { dialogs.lotw = true }
                 )
             }
@@ -582,6 +583,7 @@ private fun SwitchRow(labelResId: Int, checked: Boolean, onCheckedChange: (Boole
 private fun LoTWCard(
     settings: com.rtbishop.look4sat.core.domain.model.LoTWSettings,
     workedGridsCount: Int,
+    lastSyncEpochMs: Long,
     showLoTWDialog: () -> Unit
 ) {
     ElevatedCard(modifier = Modifier.fillMaxWidth()) {
@@ -600,6 +602,14 @@ private fun LoTWCard(
                 style = MaterialTheme.typography.bodySmall,
                 maxLines = 2
             )
+            // Last successful sync, shown exactly like the ephemeris update time.
+            if (lastSyncEpochMs != 0L) {
+                Spacer(modifier = Modifier.height(2.dp))
+                Text(
+                    text = formatUpdateTime(updateTime = lastSyncEpochMs),
+                    style = MaterialTheme.typography.bodySmall
+                )
+            }
             Spacer(modifier = Modifier.height(4.dp))
             CardButton(
                 onClick = showLoTWDialog,

feature/settings/src/main/java/com/rtbishop/look4sat/feature/settings/SettingsState.kt

@@ -65,6 +65,8 @@ data class SettingsState(
     val lotwSyncMode: LoTWSyncMode? = null,
     val lotwProgress: com.rtbishop.look4sat.core.domain.repository.LoTWProgress? = null,
     val lotwError: LoTWError? = null,
+    /** Epoch ms of the last successful LoTW sync (0 = never) — shown like the ephemeris update time. */
+    val lotwLastSyncEpochMs: Long = 0L,
     val updateChecker: UpdateCheckerState = UpdateCheckerState()
 )
 

feature/settings/src/main/java/com/rtbishop/look4sat/feature/settings/SettingsViewModel.kt

@@ -30,6 +30,8 @@ import com.rtbishop.look4sat.core.domain.repository.IUpdateRepository
 import com.rtbishop.look4sat.core.domain.repository.LoTWResult
 import com.rtbishop.look4sat.core.domain.repository.LoTWSyncMode
 import com.rtbishop.look4sat.core.domain.repository.applyLoTWGridResult
+import com.rtbishop.look4sat.core.domain.repository.lotwCursorApi
+import com.rtbishop.look4sat.core.domain.repository.lotwCursorEpochMs
 import com.rtbishop.look4sat.core.domain.repository.resolveLoTWSyncMode
 import com.rtbishop.look4sat.core.domain.repository.IWavelogRepository
 import com.rtbishop.look4sat.core.domain.usecase.IShowToast
@@ -66,7 +68,8 @@ class SettingsViewModel(
             dataSourcesSettings = settingsRepo.dataSourcesSettings.value,
             dataSourcesStatus = settingsRepo.dataSourcesStatus.value,
             wavelogSettings = settingsRepo.wavelogSettings.value,
-            workedGridsCount = settingsRepo.getWorkedGrids().size
+            workedGridsCount = settingsRepo.getWorkedGrids().size,
+            lotwLastSyncEpochMs = lotwCursorEpochMs(settingsRepo.getLastLotwSyncDate())
         )
     )
 
@@ -215,7 +218,7 @@ class SettingsViewModel(
         val callsign = settings.callsign.trim().uppercase()
         val effectiveMode = resolveLoTWSyncMode(settingsRepo.getLastLotwSyncCallsign(), callsign, mode)
         val since = if (effectiveMode == LoTWSyncMode.Incremental) {
-            settingsRepo.getLastLotwSyncDate()
+            lotwCursorApi(settingsRepo.getLastLotwSyncDate())
         } else ""
         _uiState.update {
             it.copy(lotwSyncing = true, lotwSyncMode = effectiveMode, lotwProgress = null, lotwError = null)
@@ -233,7 +236,8 @@ class SettingsViewModel(
                     _uiState.update { state ->
                         state.copy(
                             lotwSyncing = false, lotwSyncMode = null, lotwProgress = null,
-                            workedGridsCount = mergedGridsCount, lotwError = null
+                            workedGridsCount = mergedGridsCount, lotwError = null,
+                            lotwLastSyncEpochMs = lotwCursorEpochMs(settingsRepo.getLastLotwSyncDate())
                         )
                     }
                 }