feat(search-result): extend DocumentSearchResult with pageNumber/pageSize/totalPages

Rename `total` → `totalElements` for Spring-Page parity and add three new
required paging fields: pageNumber, pageSize, totalPages. Adds a `paged(
slice, pageable, totalElements)` factory alongside the existing single-page
`of(list)` shortcut. Enables offset pagination of /documents search (#315).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

backend/src/main/java/org/raddatz/familienarchiv/dto/DocumentSearchResult.java

@@ -1,6 +1,7 @@
 package org.raddatz.familienarchiv.dto;
 
 import io.swagger.v3.oas.annotations.media.Schema;
+import org.springframework.data.domain.Pageable;
 
 import java.util.List;
 
@@ -8,9 +9,30 @@ public record DocumentSearchResult(
         @Schema(requiredMode = Schema.RequiredMode.REQUIRED)
         List<DocumentSearchItem> items,
         @Schema(requiredMode = Schema.RequiredMode.REQUIRED)
-        long total
+        long totalElements,
+        @Schema(requiredMode = Schema.RequiredMode.REQUIRED)
+        int pageNumber,
+        @Schema(requiredMode = Schema.RequiredMode.REQUIRED)
+        int pageSize,
+        @Schema(requiredMode = Schema.RequiredMode.REQUIRED)
+        int totalPages
 ) {
+    /**
+     * Single-page convenience factory used by empty-result shortcuts and by tests that
+     * don't care about paging. Treats the whole list as page 0 of itself.
+     */
     public static DocumentSearchResult of(List<DocumentSearchItem> items) {
-        return new DocumentSearchResult(items, items.size());
+        int size = items.size();
+        return new DocumentSearchResult(items, size, 0, size, size == 0 ? 0 : 1);
+    }
+
+    /**
+     * Paged factory used by the service when it has a real Pageable + full match count
+     * (e.g. from Spring's Page<T> or from an in-memory sort-then-slice).
+     */
+    public static DocumentSearchResult paged(List<DocumentSearchItem> slice, Pageable pageable, long totalElements) {
+        int pageSize = pageable.getPageSize();
+        int totalPages = pageSize == 0 ? 0 : (int) ((totalElements + pageSize - 1) / pageSize);
+        return new DocumentSearchResult(slice, totalElements, pageable.getPageNumber(), pageSize, totalPages);
     }
 }