feat: deep sleep single-fetch with probabilistic weighting

Refactor timerWakeCycle() to fetch a single random photo per wake
using cycle-mode-aware server-side filtering via Immich's
POST /api/search/random endpoint.

Changes:
- Add fetchOneRandomAssetId() to ImmichClient with support for
  isFavorite, takenAfter, takenBefore filter parameters
- Add timer_last_date NVS field for chronological cursor persistence
- Implement probabilistic filter selection per cycle mode:
  - Random: unfiltered size=1
  - Chronological/ReverseChronological: date cursor in NVS
  - FavoritesWeighted: 66% favorites, 33% unfiltered
  - WeightedChronological: 66% recent (30d), 33% unfiltered
  - WeightedReverseChronological: 66% older (30d), 33% unfiltered
- Add retry loop with filter relaxation on empty results
- Initialize hardware RTC (RX8130CE) firmware-wide:
  - Seed system clock from RTC at boot (immediate time)
  - NTP sync after WiFi connect, write back to RTC
- Add time_utils.h with isoNow(), isoNowMinus30d(), hasValidTime()

Normal mode (PhotoQueue + displayTask) is completely untouched.

Co-authored-by: Cursor <cursoragent@cursor.com>

src/immich_client.cpp

@@ -211,6 +211,68 @@ std::vector<String> ImmichClient::fetchFavoriteAssetIds() {
     return ids;
 }
 
+String ImmichClient::fetchOneRandomAssetId(const RandomFetchFilter& filter) {
+    String url = buildUrl("/api/search/random");
+
+    JsonDocument reqDoc;
+    reqDoc["size"] = 1;
+    reqDoc["type"] = "IMAGE";
+
+    if (!filter.albumIds.empty()) {
+        JsonArray arr = reqDoc["albumIds"].to<JsonArray>();
+        for (auto& id : filter.albumIds) arr.add(id);
+    }
+    if (filter.favoriteOnly) {
+        reqDoc["isFavorite"] = true;
+    }
+    if (filter.takenAfter.length() > 0) {
+        reqDoc["takenAfter"] = filter.takenAfter;
+    }
+    if (filter.takenBefore.length() > 0) {
+        reqDoc["takenBefore"] = filter.takenBefore;
+    }
+
+    String body;
+    serializeJson(reqDoc, body);
+
+    Serial.printf("[immich] fetchOne: %s\n", body.c_str());
+
+    String response = httpPost(url, body);
+    if (response.isEmpty()) {
+        Serial.println("[immich] fetchOne: empty response");
+        return "";
+    }
+
+    JsonDocument doc;
+    DeserializationError err = deserializeJson(doc, response);
+    if (err) {
+        Serial.printf("[immich] fetchOne JSON error: %s\n", err.c_str());
+        return "";
+    }
+
+    JsonArray arr = doc.as<JsonArray>();
+    for (JsonObject asset : arr) {
+        String id = asset["id"].as<String>();
+        if (id.length() == 0) continue;
+
+        // Skip RAW files
+        String filename = asset["originalFileName"] | "";
+        filename.toLowerCase();
+        if (filename.endsWith(".dng") || filename.endsWith(".raw") ||
+            filename.endsWith(".cr2") || filename.endsWith(".cr3") ||
+            filename.endsWith(".nef") || filename.endsWith(".arw") ||
+            filename.endsWith(".orf") || filename.endsWith(".rw2") ||
+            filename.endsWith(".raf") || filename.endsWith(".srw")) {
+            continue;
+        }
+
+        return id;
+    }
+
+    Serial.println("[immich] fetchOne: no usable asset returned");
+    return "";
+}
+
 AssetInfo ImmichClient::fetchAssetInfo(const String& assetId) {
     AssetInfo info;
     info.id = assetId;