Right, basically the generalization goes: Lie groups -> Lie group actions -> Lie groupoids. This is not a new observation (in fact Arnold’s fluid mechanics can be rephrased using lie groupoids https://tspace.library.utoronto.ca/bitstream/1807/91859/1/Fu..., and big names like Alan Weinstein have worked in that area). I don’t think the authors actually understand that story, so they very naively went groups -> group actions -> monads. If it went that way someone in mathematical physics or optimization would have stumbled onto other concrete examples. But they haven’t, because it doesn’t.