I agree this needs to be reframed but suggest that assignment in place isn't the most useful mental model.
Instead, something like "generically apply a value to another" (dunder apply) or "update an object with another" (dunder update) might have a prayer of making sense. Perhaps there are other situations where having a *generic* operator meant to communicate the concept of sending and object into another makes sense. A few come to mind:
It's worth considering whether there would be benefit in providing a generic operator that provides nice syntax, intended for general use dependent entirely on that the user wants to make it mean. And whether some of the existing functionality above might benefit from some prettier syntax as well.