>> Yes, this is a harder problem.  We have to remember meta-data for
>> every search history element.  There are several possibilities:
>>
>> 4. Adding meta-data by text-properties to the strings in
>>    ‘search-ring’ and ‘regexp-search-ring’ poses a problem of saving
>>    the values in the desktop and restoring in another session.
>
> This feels like the best solution. I looked at desktop.el, and it
> doesn't save the properties, as you say. But it could be made to. Do you
> think some external packages would get broken by this change?

This seems to be the least radical change as concluded in
https://lists.gnu.org/archive/html/emacs-devel/2018-03/msg00296.html
The patch makes the search mode to be remembered in isearch as well as
in query-replace.