Ripple is mentioned in this documentation page: Glossary / Terminology
It works for me, but perhaps you are using terminology loosely. Cut is something very specific because there is a UI action with that label. Lift and Split do not ripple; so there is nothing to affect on another track.
You have to option to “detach audio” but not to attach it back to the video - should be possible?
Simply remove the audio clip, and on the video clip choose Properties > Audio > Track. In case you had filters on the audio clip, you can copy and paste them to the video clip.