Hi Dmitry,

> Thanks for working on this.
>
>> +				(replace-search search-string limit
>> +						regexp-flag delimited-flag
>> +						case-fold-search backward))
>
> I don't know this code too well, but perhaps SEARCH_STRING here should be
> anchored with something like "\\=" at the beginning?
>
> Otherwise the search can succeed here even if the next match is not
> here. Not sure how important that is, though.

Stefan confirmed that "\\=" is reliable.  Thanks for the suggestion.
Now everything is ready.  Please try the latest patch in bug#14013
together with the patch for xref.el below.  I've tested with your
test cases from bug#53758, and everything works well.

>> -         ;; Counteract the "do the next match now" hack in
>> -         ;; `perform-replace'.  And still, it'll report that those
>> -         ;; matches were "filtered out" at the end.
>> -         (isearch-filter-predicate
>> -          (lambda (beg end)
>> -            (and current-beg
>> -                 (>= beg current-beg)
>> -                 (<= end current-end))))
>
> Please note that we'll likely have to keep this code here for a number of
> Emacs releases. So the patch should be tested with both versions: with this
> code present and with it removed, to ensure present and future
> compatibility.

I guess this might need more conditionals like (>= emacs-major-version 29).