I’m not sure whether to classify this as a bug or not, but it seemed like the closest fit.
Simply put, Aseprite beta v1.3 does not display the Preview window in recording software such as SLOBS / OBS when doing a window capture. You can still see your mouse interacting with it, but not the window itself, regardless of whether the preview window is within the bounds of the main aseprite window or not.
The preview window appears fine in the current stable build, so I’m assuming the change to make it detach has caused the issue. Would be nice if the preview window at least showed again while within the confines of the main aseprite window, but it would be ideal if it was considered its own window when outside of the main aseprite window so that you can designate it specifically for window capture by recording software.