refactor: split pagination logic from response models

- Extract pagination logic to separate util module
- Update response models to use new pagination util
- Fix pagination calculation edge cases

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/tests/test_utils/test_pagination.py

@@ -102,3 +102,38 @@ class TestComputeTotalPages:
 
         with pytest.raises(ValueError, match="page_size must be >= 1"):
             compute_total_pages(100, -1)
+
+
+class TestPaginationMetadataMode:
+    """Test pagination_mode field in create_pagination_metadata."""
+
+    def test_create_pagination_metadata_sets_offset_mode(self) -> None:
+        """create_pagination_metadata sets pagination_mode to 'offset'."""
+        from app.utils.pagination import create_pagination_metadata
+
+        metadata = create_pagination_metadata(total=100, page=2, page_size=10)
+        assert metadata.pagination_mode == "offset"
+
+    def test_create_keyset_pagination_metadata_sets_cursor_mode(self) -> None:
+        """create_keyset_pagination_metadata sets pagination_mode to 'cursor'."""
+        from app.utils.pagination import create_keyset_pagination_metadata
+
+        metadata = create_keyset_pagination_metadata([], None, 10)
+        assert metadata.pagination_mode == "cursor"
+
+    def test_cursor_metadata_has_cursor_none_when_no_next_page(self) -> None:
+        """Cursor metadata with no next page has cursor=None and has_next_page=False."""
+        from app.utils.pagination import create_keyset_pagination_metadata
+
+        metadata = create_keyset_pagination_metadata([], None, 10)
+        assert metadata.has_next_page is False
+        assert metadata.cursor is None
+
+    def test_cursor_metadata_has_next_page_when_cursor_present(self) -> None:
+        """Cursor metadata with next_cursor sets has_next_page=True."""
+        from app.utils.pagination import create_keyset_pagination_metadata, encode_cursor
+
+        next_cursor = encode_cursor(42)
+        metadata = create_keyset_pagination_metadata([{"id": 42}], next_cursor, 10)
+        assert metadata.has_next_page is True
+        assert metadata.cursor == next_cursor