I have now tried many different text strings in this StartupWMClass on my two Octave .desktop files. And I always restarted the Gnome session inbetween. Result: I never managed to have both .desktop icons work at the same time. Currently always Octave 7.0.90 is pinned, regardless if I start the 7.0.90 .desktop file of if I start the 6.3.0 .desktop file. (The initially starting Octave program version is correct on both cases, it is just the wrong link added to the task bar afterwards for one of them.)

My personal conclusion is now, that this is most probable a Gnome (or similar) problem that has nothing to do with Octave. Maybe it is also not ment to be possible to start two different Octave versions both by desktop icons on the task bar. I am not sure is is worth to further bother with this...

Maybe without logout: https://unix.stackexchange.com/questions/12118/how-do-i-refresh-gnome-3-applications

When I change the StartupWMClass text string in the .destop file to something else than "GNU Octave" then I cannot pin the resulting destop icon to the task bar at all any more. I chose "GNU Oct" and "GNU Octa" for this string in my two .destop files. And now neither of the started Octave versions still offers the entry "add to favorites" on a task bar right click any more. Also I now get a task bar icon that seems to have much less pixel resultion in both cases as well.

My conclusion: There seems to be something "magic" with the content "GNU Octave" in the StartupWMClass text string, other text strings do not work at all for me.

1. I have only installed Octave 6.3.0 and 7.0.90 on this computer, both by downloading the tar.gz file of the release (or pre-release) into a folder in /opt with user write access, and then did "configure", "make" and "make install" there (without any sudo). I have not installed any Octave version by the package manager on this machine at all. I have also not installed any Octave version via flatpack or snap.

2. This is under Ubuntu 20.04 LTS linux with german locale. This Ubuntu is quite freshly installed (a few months ago) and still more or less "vanilla". It uses the default Gnome desktop.

3. My two corresponding .desktop files are generated "by hand" in my text editor and look like this:

#!/usr/bin/env xdg-open

[Desktop Entry]
Version=1.0
Type=Application
Terminal=false

Name=Octave 7.0.90 (opt)
Exec=/opt/octave-7.0.90/bin/octave --gui %f
Icon=/opt/octave-7.0.90/libgui/src/icons/logo.png

StartupNotify=false
StartupWMClass=GNU Octave
MimeType=text/x-octave;text/x-matlab;

When I save the above file content to a file with the file name "Octave 7.0.90 (opt).desktop", set the execution bit, and then start it and try to pin the icon to the Gnome task bar, then the akward behavior described in comment #0 happens. (I have exactly one other .desktop file, for Octave versions 6.3.0 in my ./local/share/applications folder. It looks the very same, just substitute 7.0.90 by 6.3.0.)

I am not sure if this is rather a bug in Gnome and not in Octave.

When I start Octave 7.0.90 like normal (for me this is a .desktop file in ./local/share/applications that points to the relevant /bin/octave --gui), then the GUI opens properly and the Octave icon is properly display on my (Gnome) task bar.

But "pinning" this icon to the task bar (under Gnome with a right mouse click, and then "add to favorites") does not have the intended effect. The task bar icon is pinned. But when I click it the next time, a different (installed) version of Octave (version 6.3.0) is opening up instead of the version 7.0.90 which is mentioned in the .desktop file.

Am I the only one seeing this behavior? Am I doing something wrong here, or is there some meta-information missing somewhere, so that linux can tell that the new Octave binary version is a different program to the last version of Octave?