What happens is that when you connect a Logitech mouse or keyboard to a Windows 7/10/11 machine for the first time, Windows Update doesn't just download a driver (a .inf file) but also Logitech Download Assistant (a .dll file) and runs it.

You will then get a branded popup in the system tray prompting you to download the actual control software.

The LDA software is set to always run in the background, it also doesn't show up in add/remove programs, and is rather annoying to get rid of.