Is it possible to find out the current/most-recent channel?

Is there a way to use the plugin to ask a Harmony Hub what channel it's currently on? And/or, can you listen for notifications from the hub and if it's a channel change perform some action?

Sorry, no to both. The plugin has no way to query the hub for anything. All it can do is send commands and listen for state changes that the hub broadcasts. And it appears that the hub does not send any updates for either channel up/down commands or direct tuning.