This is now implemented! Mailspring 1.19.1 upgraded to Electron 41, which enabled Windows toast notifications with proper action buttons — including inline reply, Archive, and Mark as Read — that work without opening the main window.
Mailspring 1.20.0 then fixed a race condition that was causing these buttons to be unreliable in some cases. If you were seeing the buttons appear but not always work, updating to 1.20.0 should resolve that.