Hmm. If "System Preferences > General > Close windows when quitting an app" is checked, and Login Items is empty, and "Reopen windows when logging back in" is unchecked when you restart or shut down, then I'd start to wonder about the possibility of either malware or some kind of helper application I might have installed without thinking about it.
Have you tried opening Activity Monitor right after starting up, noting anything unusual in the Process Name list, and looking that up online? (Lots of processes with unfamiliar names belong to macOS, but maybe there's something there…?)