I'm having the same predicament. I don't want or need the LogiOptions or any other downloader installing and running itself independently. I paired a Logitech BlueTooth mouse with a laptop that had a brand new and clean Windows 11 2026H2 running. The next day there are two separate Logitech applications that appear in my Installed Apps list that I did not install or even download myself. Now the same update ["Logitech SoftwareComponent Driver Update (2.0.1020.0)" ] is pending in my Windows Updates.
I've uninstalled the Logitech apps. When I try to use the deprecated "show/hide updates" utility above, it can see a couple of other pending updates, but the Logitech entry is not included. I tried another tip using a PowerShell command that also surfaces pending updates. This picked the same updates as the utility, and also did not find or include this pending Logitech update, so you can't even hide/block this update using the standard PowerShell approach.
It seems like Logitech has gone through some effort here to make sure that consumers and even system admins cannot easily sidestep the auto-download-and-silently-install-and-then-always-run-at-startup nature of their "driver" packages that are more like full-scale software suites. And you can't even argue that this makes the device more secure. Autostarting background software increases the attack surface much more than a basic and static INF file ever would, at least when it comes to the functions of a relatively simple wireless mouse.