Do you still have 7.6 installed?

I don't think this is related to the use of AppImage.
I am on Ubuntu 22.04 + GNOME 42.9 and I have a similar issue. Interestingly, it depends on the component:

- opening Writer 24.2 shows "7.6" in the dock (bad)
- opening Impress or Draw 24.2 shows "24.2" in the dock (OK)
- opening Writer 7.6 shows "7.6" in the dock (OK)
- opening Impress or Draw 7.6 shows "24.2" in the dock (bad)
- opening Calc or Math (regardless of version) shows the old Calc or Math icon in the dock, no version in tooltip (bad)
- opening the Start Center (regardless of version) shows me 24.8 in the dock (the dev version I've also installed from deb) (bad)

A bit of a mixed bag!

Version: 24.2.0.3 (X86_64) / LibreOffice Community
Build ID: da48488a73ddd66ea24cf16bbc4f7b9c08e9bea1
CPU threads: 8; OS: Linux 6.5; UI render: default; VCL: gtk3
Locale: en-AU (en_AU.UTF-8); UI: en-US
Calc: threaded

I don't know if it's a Wayland issue, possibly related to bug 125934.
But launching in a MetaWindowXwayland does not fix it.

Michael, what do you think?

2 things I can think of that *might* be relevant here:

1) The use of themed application icons, i.e. depending on what icon theme is in use (likely set in GNOME or KDE system settings), the icons from that theme may be preferred, not any shipped with LibreOffice.

2) The .desktop files from underneath $XDG_DATA_DIRS (see the desktop entry spec: [1]), like /usr/share/applications/libreoffice-startcenter.desktop or /usr/share/applications/libreoffice-writer.desktop
From what I know, in particular on Wayland, the app-id set for the "window" (might be called "surface" in Wayland terminology, but I'm not sure) is used to associate the window with a desktop entry, and window managers/Wayland compositors/task bar entry managers use the icon (and maybe more data) from these.

Example: 

app-id is set to "libreoffice-writer"
-> corresponding desktop file is /usr/share/applications/libreoffice-writer.desktop

The desktop file has an entry "Icon=libreoffice-writer" -> An icon with that name is used, presumably preferring the one from the currently set icon theme.

On my Debian testing, that desktop file also has an entry "Name=LibreOffice Writer", and that's what I see when hovering over the taskbar entry in my KDE Plasma X11 session on Debian testing when starting the Debian-provided LibreOffice Writer.

Do your desktop files contain any "Name=" entry that contains the version number?

I don't know about all of the details and there might be other things that come into play.
Not sure what of the current behavior would then even be correct from a technical perspective ("works as designed"), as e.g. supporting theming generally seems to be a good idea in my eyes.
One way to override the current behavior that might possibly work is to prepend a directory containing own .desktop files to XDG_DATA_DIRS so that one is checked first. (Might have to be done on session start as the process managing the taskbar likely uses its own environment and not environment variables set only on LO start.)

[1] https://specifications.freedesktop.org/desktop-entry-spec/desktop-entry-spec-latest.html

(In reply to Michael Weghorn from comment #2)
> On my Debian testing, that desktop file also has an entry "Name=LibreOffice
> Writer", and that's what I see when hovering over the taskbar entry in my
> KDE Plasma X11 session on Debian testing when starting the Debian-provided
> LibreOffice Writer.
> 
> Do your desktop files contain any "Name=" entry that contains the version
> number?

I just changed the "Name" entry in /usr/share/applications/libreoffice-startcenter.desktop to "Name=LibreOffice Test123" and started the AppImage version and then "LibreOffice Test123" is actually shown as the name when hovering over the taskbar entry of the LO StartCenter window in my Plasma X11 session.