Estimate progress while rsync scans from the last backup's file count

With incremental recursion rsync only knows the total near the end, so the bar showed
no ETA for most of the backup. Save the file count as a third line of the state file
and use it as an estimate until rsync reports the real total.

tests/test_cli.py

@@ -32,7 +32,8 @@ class FakeBackup:
     def __init__(self, inputs: Any, output: Any, exclude: Any, keep: Any, options: str,
                  ssh_host: str | None = None, ssh_user: str | None = None,
                  ssh_keyfile: str | None = None, remote_sudo: bool = False,
-                 remove_before: bool = False, verbose: bool = False, progress: bool = False) -> None:
+                 remove_before: bool = False, verbose: bool = False, progress: bool = False,
+                 file_estimate: int = 0) -> None:
         self.inputs = inputs
         self.output = output
         self.exclude = exclude
@@ -45,6 +46,8 @@ class FakeBackup:
         self.remove_before = remove_before
         self.verbose = verbose
         self.progress = progress
+        self.file_estimate = file_estimate
+        self.file_count: int | None = None
         self.homedir: str | None = None
         self.ran = False
         self.closed = False
@@ -87,7 +90,7 @@ def as_root(monkeypatch: pytest.MonkeyPatch) -> None:
 
     monkeypatch.setattr(os, 'geteuid', lambda: 0)
     # Writing the state file as root would call seteuid() (covered in test_state.py)
-    monkeypatch.setattr(sb, '_write_state', lambda user, destination: None)
+    monkeypatch.setattr(sb, '_write_state', lambda user, destination, file_count=None: None)
 
     for var in ['SUDO_USER', 'SUDO_UID', 'DOAS_USER']:
         monkeypatch.delenv(var, raising=False)
@@ -266,6 +269,17 @@ ssh_keyfile=/keys/id
         assert run_cli('-c', config('backup_dir=/backups'), *argv) == 0
         assert last_backup().progress is progress
 
+    @pytest.mark.parametrize('tty, estimate', [(True, 1234), (False, 0)])
+    def test_file_estimate(self, run_cli: RunCli, config: Callable[[str], str], monkeypatch: pytest.MonkeyPatch,
+                           tmp_path: Path, tty: bool, estimate: int) -> None:
+        monkeypatch.setattr(sb.sys.stderr, 'isatty', lambda: tty)
+        state = tmp_path / 'state' / 'simple_backup' / 'last_backup'
+        state.parent.mkdir(parents=True)
+        state.write_text('2026-10-25T10:00:00+02:00\n/backups/old\n1234\n')
+
+        assert run_cli('-c', config('backup_dir=/backups')) == 0
+        assert last_backup().file_estimate == estimate
+
     def test_check_params_failure(self, run_cli: RunCli, config: Callable[[str], str]) -> None:
         FakeBackup.check_code = 2