add session-gated /sync endpoint and prune stale vectors after reindex

SyncController/SyncService/SyncProvider mirror the existing search
dispatch pattern: a session-gated controller routes a SyncRequest to
the provider registered for its ServiceType. HomeboxSyncProvider pages
through the full Homebox catalog, embedding each page via
EmbeddingService, and now collects every item ID it sees across all
pages before pruning anything no longer present upstream in one
deleteStaleVectorEntries call at the end - deleting per page would
treat items on other pages as stale and wipe them out.

backend/src/main/java/com/vaessl/app/sync/HomeboxSyncProvider.java

@@ -1,27 +1,57 @@
 package com.vaessl.app.sync;
 
-import org.springframework.stereotype.Service;
+import java.util.ArrayList;
+import java.util.List;
+import org.springframework.data.domain.Page;
+import org.springframework.data.domain.PageRequest;
+import org.springframework.data.domain.Pageable;
+import org.springframework.stereotype.Component;
+import com.vaessl.app.homebox.HomeboxItemClient;
+import com.vaessl.app.homebox.HomeboxItemClient.HomeboxItemPage;
+import com.vaessl.app.shared.ServiceItem;
 import com.vaessl.app.shared.ServiceType;
 import com.vaessl.app.vector.EmbeddingService;
+import lombok.RequiredArgsConstructor;
 
-@Service
+/**
+ * Pages through the full Homebox catalog and re-indexes it into the vector store.
+ * Item IDs are collected across all pages before {@link EmbeddingService#deleteStaleVectorEntries}
+ * is called once at the end, rather than after each page: deleting per page would treat every
+ * item outside the current page as stale, wiping out entries from pages already synced.
+ */
+@Component
+@RequiredArgsConstructor
 public class HomeboxSyncProvider implements SyncProvider {
 
     private final EmbeddingService embeddingService;
 
-    public HomeboxSyncProvider(EmbeddingService embeddingService) {
-        this.embeddingService = embeddingService;
-    }
-    
+    private final HomeboxItemClient client;
+
     @Override
     public ServiceType getServiceType() {
         return ServiceType.HOMEBOX;
     }
 
     @Override
-    public void syncVectorStore() {
-        // TODO Auto-generated method stub
-        throw new UnsupportedOperationException("Unimplemented method 'syncVectorStore'");
-    }
+    public void syncVectorStore(SyncRequest request) {
 
+        int batchSize = 100;
+        int page = 0;
+        Page<ServiceItem> current;
+        Long connectionId = null;
+        List<String> currentItemIds = new ArrayList<>();
+        do {
+            Pageable pageable = PageRequest.of(page, batchSize);
+            HomeboxItemPage result = client.hbResponse(request, null, pageable);
+            current = result.page();
+            if (connectionId == null) {
+                connectionId = result.connectionId();
+            }
+            embeddingService.vectorizeData(current.getContent(), request.serviceType(),
+                    result.connectionId(), currentItemIds);
+            page++;
+        } while (page < current.getTotalPages());
+
+        embeddingService.deleteStaleVectorEntries(connectionId, currentItemIds);
+    }
 }