The option dired-kill-when-opening-new-dired-buffer is not respected
when clicking on parent directories in the directory line at the top of 
dired
buffers.  This can be fixed by calling
dired--find-possibly-alternate-file instead of dired in the callback, as
my attached patch does.

I believe changing to dired--find-possibly-alternate-file is safe 
because from
playing around with dired, the directory being clicked on must be a 
directory
and can not contain wildcards at this point.  Therefore, at this point 
it is
known that the directory is just a plain directory (no wildcards) and so 
going
through find-file machinery will have the intended result.

Steps to reproduce:

emacs -Q
M-x load-library RET dired RET
M-x set-variable RET dired-kill-when-opening-new-dired-buffer RET t RET
C-x d ~/ RET
Click something in the directory line like "home" in "/home/jared" for 
myself.
C-x C-b
See that there are two directory buffers instead of just one.

In GNU Emacs 29.1 (build 2, x86_64-pc-linux-gnu, GTK+ Version 3.24.37,
  cairo version 1.16.0) of 2023-09-11, modified by Debian built on melete
System Description: Debian GNU/Linux 12 (bookworm)

Configured using:
  'configure --build x86_64-linux-gnu --prefix=/usr
  --sharedstatedir=/var/lib --libexecdir=/usr/libexec
  --localstatedir=/var/lib --infodir=/usr/share/info
  --mandir=/usr/share/man --with-libsystemd --with-pop=yes
  
--enable-locallisppath=/etc/emacs:/usr/local/share/emacs/29.1/site-lisp:/usr/local/share/emacs/site-lisp:/usr/share/emacs/29.1/site-lisp:/usr/share/emacs/site-lisp
  --with-sound=alsa --without-gconf --with-mailutils
  --with-native-compilation --build x86_64-linux-gnu --prefix=/usr
  --sharedstatedir=/var/lib --libexecdir=/usr/libexec
  --localstatedir=/var/lib --infodir=/usr/share/info
  --mandir=/usr/share/man --with-libsystemd --with-pop=yes
  
--enable-locallisppath=/etc/emacs:/usr/local/share/emacs/29.1/site-lisp:/usr/local/share/emacs/site-lisp:/usr/share/emacs/29.1/site-lisp:/usr/share/emacs/site-lisp
  --with-sound=alsa --without-gconf --with-mailutils
  --with-native-compilation --with-pgtk 'CFLAGS=-g -O2
  -ffile-prefix-map=/build/emacs-N816CI/emacs-29.1+1=. 
-fstack-protector-strong
  -Wformat -Werror=format-security -Wall' 'CPPFLAGS=-Wdate-time
  -D_FORTIFY_SOURCE=2' LDFLAGS=-Wl,-z,relro'

Configured features:
ACL CAIRO DBUS FREETYPE GIF GLIB GMP GNUTLS GPM GSETTINGS HARFBUZZ JPEG
JSON LCMS2 LIBOTF LIBSELINUX LIBSYSTEMD LIBXML2 MODULES NATIVE_COMP
NOTIFY INOTIFY PDUMPER PGTK PNG RSVG SECCOMP SOUND SQLITE3 THREADS TIFF
TOOLKIT_SCROLL_BARS TREE_SITTER WEBP XIM GTK3 ZLIB

Important settings:
   value of $LANG: en_US.UTF-8
   locale-coding-system: utf-8-unix

Major mode: Dired by name

Minor modes in effect:
   tooltip-mode: t
   global-eldoc-mode: t
   show-paren-mode: t
   electric-indent-mode: t
   mouse-wheel-mode: t
   tool-bar-mode: t
   menu-bar-mode: t
   file-name-shadow-mode: t
   global-font-lock-mode: t
   font-lock-mode: t
   blink-cursor-mode: t
   buffer-read-only: t
   line-number-mode: t
   indent-tabs-mode: t
   transient-mark-mode: t
   auto-composition-mode: t
   auto-encryption-mode: t
   auto-compression-mode: t

Load-path shadows:
None found.

Features:
(shadow sort mail-extr emacsbug message mailcap yank-media puny rfc822
mml mml-sec password-cache epa derived epg rfc6068 epg-config gnus-util
text-property-search time-date mm-decode mm-bodies mm-encode mail-parse
rfc2231 mailabbrev gmm-utils mailheader sendmail rfc2047 rfc2045
ietf-drums mm-util mail-prsvr mail-utils mule-util display-line-numbers
dired-aux cus-edit pp cus-start cus-load wid-edit help-fns radix-tree
dired dired-loaddefs thingatpt cl-loaddefs comp comp-cstr warnings icons
subr-x rx cl-seq cl-macs gv cl-extra help-mode bytecomp byte-compile
cl-lib find-func rmc iso-transl tooltip cconv eldoc paren electric
uniquify ediff-hook vc-hooks lisp-float-type elisp-mode mwheel
term/pgtk-win pgtk-win term/common-win pgtk-dnd tool-bar dnd fontset
image regexp-opt fringe tabulated-list replace newcomment text-mode
lisp-mode prog-mode register page tab-bar menu-bar rfn-eshadow isearch
easymenu timer select scroll-bar mouse jit-lock font-lock syntax
font-core term/tty-colors frame minibuffer nadvice seq simple cl-generic
indonesian philippine cham georgian utf-8-lang misc-lang vietnamese
tibetan thai tai-viet lao korean japanese eucjp-ms cp51932 hebrew greek
romanian slovak czech european ethiopic indian cyrillic chinese
composite emoji-zwj charscript charprop case-table epa-hook
jka-cmpr-hook help abbrev obarray oclosure cl-preloaded button loaddefs
theme-loaddefs faces cus-face macroexp files window text-properties
overlay sha1 md5 base64 format env code-pages mule custom widget keymap
hashtable-print-readable backquote threads dbusbind inotify
dynamic-setting system-font-setting font-render-setting cairo gtk pgtk
lcms2 multi-tty make-network-process native-compile emacs)

Memory information:
((conses 16 105919 13638)
  (symbols 48 9060 0)
  (strings 32 24805 2351)
  (string-bytes 1 725024)
  (vectors 16 17316)
  (vector-slots 8 354985 19128)
  (floats 8 37 33)
  (intervals 56 711 0)
  (buffers 984 14))