I was unable to find a combination of settings in either Factorio or Logitech that didn't result in the lights turning off when alt-tabbing and then refocusing the game (even directly from the main menu immediately after launching the game). I could find no real difference between your settings and ...

I still encounter this issue on Factorio v. 1.1.69 with Logitech G-Hub v. 2022.8.306864 (released Aug 30, 2022) and a G512 keyboard. The lights are lit up in the Factorio color until I alt-tab, at which point they switch to the normal colors as expected when Factorio loses focus. Once Factorio is ...