bug#81561: 31.0.91; speedbar-window-mode creates stale idle timers

The new `speedbar-window-mode' (Emacs 31) leaves stale idle timers
around. In order to reproduce:

1. emacs -Q
2. M-x speedbar-window-mode (repeat a few times)
3. M-x list-timers => Multiple idle timers are present
   (dframe-timer-fn) while there should only be a single one.

Alternatively:

1. emacs -Q
2. (setq speedbar-prefer-window t)
3. M-x speedbar (repeat a few times)
4. M-x list-timers => Multiple idle timers are present
   (dframe-timer-fn) while there should only be a single one.

When testing with frames (without speedbar-window-mode) I don't observe
the problem and there is always only a single dframe-timer-fn idle
timer.

In GNU Emacs 31.0.91 (build 1, x86_64-pc-linux-gnu, GTK+ Version
 3.24.49, cairo version 1.18.4) of 2026-07-30
Windowing system distributor 'The X.Org Foundation', version 11.0.12101016
System Description: Debian GNU/Linux 13 (trixie)

Configured using:
 'configure --prefix=$HOME/.local/share/emacs-install
 --without-compress-install --with-tree-sitter=ifavailable
 --with-native-compilation --with-dbus --without-selinux
 --without-threads --disable-gc-mark-trace --without-gsettings
 --without-gpm --with-cairo --with-cairo-xcb --with-xinput2
 --with-x-toolkit=gtk3 --without-toolkit-scroll-bars 'CFLAGS=-O3
 -mtune=native -march=native''

Configured features:
CAIRO DBUS FREETYPE GIF GLIB GMP GNUTLS HARFBUZZ JPEG LIBOTF LIBSYSTEMD
LIBXML2 MODULES NATIVE_COMP NOTIFY INOTIFY PDUMPER PNG RSVG SECCOMP
SOUND SQLITE3 TIFF TREE_SITTER WEBP X11 XCOMPOSITE XDBE XFIXES XIM
XINERAMA XINPUT2 XPM XRANDR XRENDER XSHAPE XSYNC GTK3 ZLIB