Change system settings (such as Dark Mode, LPM, etc.)
Set and change timers and alarms
Changing to the next/previous tracks
All other Siri inquiries, such as requesting to play a specific song, sending a message or asking a question, you do need an active internet connection.
Now, Siri does process all of your audio data on device, rather than sending all of your audio information to Apple like they used to. This offline processing wasn't really made so that Siri had an expanded offline feature list, but rather to keep your voice recordings extra private. These few offline commands are just a side effect of that.