>> (progn
>>   (setopt isearch-wrap-pause 'no)
>>   ;; (setopt isearch-wrap-pause 'no-ding)  ; this causes the same problem
>>   (with-current-buffer (generate-new-buffer "isearch-wrap-pause-test")
>>     (insert "bar")
>>     (goto-char (point-min))
>>     (pop-to-buffer (current-buffer))))
>>
>> ...run isearch for "baz" with...
>>
>> C-s b a z
>>
>> ...then attempt to delete the non-matching "z" character with DEL.
>>
>> GNU Emacs 29.1 (build 1, x86_64-pc-linux-gnu, GTK+ Version 3.24.37,
>> cairo version 1.16.0)
>
> Juri, could you please look into this?  It seems to be a regression in
> Emacs 29.1 due to your changes in commit 7320a812e, to solve
> bug#56535.  I guess we need to distinguish between self-inserting
> characters and DEL?

This means that we need to preclude 'isearch-push-state' in 'isearch-repeat'
from updating 'isearch-cmds'.

Should I push this patch to the emacs-29 branch?  It looks safe.