Do I know the moment when offline bouncing end?

Now I’m using Reaper daw, and I wonder that can know when offline bouncing end?

any call back function, or variable?

Please bear in mind that things aren’t that simple!

Many DAWs will do rendering + live playback at the same time. Tracktion certainly will. Maybe even multiple renders that end at different times, involving different plugin instances. You can check whether an individual plugin instance is currently being used in offline mode though, so that might be enough to do what you need.