> I wonder why ‘isearch-mode-end-hook-quit’ is not initialized as
> ‘(and nopush edit)’ in the first place?  If it was so, then
> you could just check for it in ‘multi-isearch-end’.

My understanding about that variable (i may be wrong) is that is should
be non nil just when the user quit the search with
C-g
we dont want this variable being non nil in the case of editing the string
with the idea to resume the same kind of search.

> have you tried to re-initialize multi-isearch on resuming isearch
> after exiting from the minibuffer?  (This could be achieved by
> remembering its state variables).

I like your proposal: this way is more consistent with the original code.
See attached new patch.