Android has an API that lets you run an activity when the user long-presses the home button even when you’re outside the app - Intent | Android Developers. It basically replaces the “Google assistant” app and lets you run whichever app you want instead (if that app supports the ASSIST intent, that is)
Open Tasks is an open-source Android to-do list app that syncs with cloud services.
The task is about adding Assist support to Open Tasks. When set up properly, pressing and holding the Home button on Android would bring up the “create task” activity from Open Tasks.