Save the last successful backup and add --last-backup

Write the completion time and backup directory to
$XDG_STATE_HOME/simple_backup/last_backup after each successful backup
(as the target user when run as root), for status bar reminders.
--last-backup prints it.

man/simple_backup.1

@@ -145,6 +145,11 @@ needs to be allowed to run without password in the same way.
 .TP
 .B \-\-numeric\-ids
 Use rsync \-\-numeric\-ids option. This causes rsync to use numeric uid/gid instead of trying to map uid/gid names from the local machine to the server.
+.TP
+.B \-\-last\-backup
+Print the date and directory of the last successful backup, then exit. The exit status is 0, or 1
+if no backup has been recorded yet or the state file can\(aqt be read (see
+.BR FILES ).
 .SH CONFIGURATION
 An example configuration file is provided at \(aq/usr/share/doc/simple_backup/simple_backup.conf\(aq.
 Copy it to the default location ($HOME/.config/simple_backup) and edit it as needed.
@@ -216,6 +221,16 @@ SSH connection failed.
 .TP
 .B 6
 Bad configuration file or options (for example, only one of SSH host and SSH user specified).
+.SH FILES
+.TP
+.I $XDG_STATE_HOME/simple_backup/last_backup
+Written after each successful backup (local or remote), replacing the previous one. The first line
+is the completion time in ISO 8601 format with the UTC offset (for example
+\(aq2026\-10\-25T14:03:12+02:00\(aq), the second line the backup directory (prefixed with
+\(aquser@host:\(aq for remote backups). The default location is
+\fI~/.local/state/simple_backup/last_backup\fR. When running as root with sudo, doas or \-\-user,
+the file is written to that user\(aqs \fI~/.local/state\fR and owned by them. Useful for scripts
+that remind you when a backup is overdue.
 .SH SEE ALSO
 .BR rsync (1)
 .SH AUTHORS