HOSTEX.SBR refinement: a new suffix character, "^", allows for a slight variation in the Windows behavior that you otherwise would get without specifying any suffix character. In both cases, the parent session waits for the child to exit, but in the case of the "^" suffix, it does not try to get the focus back when the child returns, and it doesn't notify any sibling A-Shell sessions when the user transmits keystrokes or mouse events while waiting that are ignored by the child while the parent is waiting.
This addresses an exotic situation with child processes that have no user interface support but which take long enough that it becomes likely for the user to either switch to another session in the meantime, or to try mouse or keyboard actions in the suspended parent session which then interfered with a sibling A-Shell session.