Link: https://support.logi.com/hc/en-us/articles/37493733117847-Options-and-G-HUB-macOS-Certificate-Issue

Turns out my mouse not working was the result of a certificate expiring in the app used to configure it, why is the Logi Options app a website?

Not many folk realise that Options+ (which is Electron based) doesn't need to be running for Logi peripherals to function, the app just has to be there and run once to let the OS know about the drivers tucked inside – the OS will use them if Options+ is running or not.
(The coders at Logi did something that when the browser-core certificate expired it effectively reset all device settings back to default, which of course were sent out to all connected devices, and then shuts itself down.)