Show elapsed time as (h:)mm:ss and add it to the notification

Replace the timing decorator with a start time kept by Backup.run(), so the final
notification can report how long the backup took.

tests/test_local.py

@@ -88,6 +88,18 @@ class TestRsync:
         assert 'Backup completed' in caplog.text
         assert 'rsync: sent' in caplog.text
 
+    def test_elapsed_time(self, src: Path, out: Path, monkeypatch: pytest.MonkeyPatch,
+                          caplog: pytest.LogCaptureFixture) -> None:
+        notifications: list[str] = []
+        monkeypatch.setattr(sb, '_notify', notifications.append)
+        # Start, then the notification and the log line
+        monkeypatch.setattr(sb, 'default_timer', iter([0.0, 863.187, 863.2]).__next__)
+
+        assert run_backup(out, [str(src)]) == 0
+
+        assert notifications[-1] == 'Backup completed in 14:23'
+        assert 'Elapsed time: 14:23' in caplog.text
+
     def test_hard_links(self, src: Path, out: Path) -> None:
         assert run_backup(out, [str(src)]) == 0
         (src / 'changed.txt').write_text('second')
@@ -231,6 +243,13 @@ class TestReadRecords:
         assert list(sb._read_records(stream)) == ['file', '', 'namé', '�']
 
 
+@pytest.mark.parametrize(('seconds', 'text'), [
+    (0.4, '00:00'), (59.6, '01:00'), (863.187, '14:23'), (3599.4, '59:59'), (3600, '1:00:00'), (37230, '10:20:30'),
+])
+def test_format_duration(seconds: float, text: str) -> None:
+    assert sb._format_duration(seconds) == text
+
+
 class TestProgressBar:
     @pytest.fixture(autouse=True)
     def terminal(self, monkeypatch: pytest.MonkeyPatch) -> None: