General: how to launch a firefox window with a different icon?

General question, specifically I am using Librewolf flatpak but this doesnt matter.

I have a desktop entry like this:

[Desktop Entry]
Name=LibreWolf
Exec=/usr/bin/flatpak run --branch=stable --arch=x86_64 --command=librewolf --file-forwarding io.gitlab.librewolf-community @@u %u @@
Comment=A fork of Firefox, focused on privacy, security and freedom.
Icon=io.gitlab.librewolf-community
Type=Application
MimeType=text/html;text/xml;application/xhtml+xml;x-scheme-handler/http;x-scheme-handler/https;application/x-xpinstall;application/pdf;application/json;
StartupWMClass=librewolf
Categories=WebBrowser;
X-MultipleArgs=false
Keywords=Internet;WWW;Browser;Web;Explorer;
Actions=X;new-private-window;profilemanager;
X-Flatpak=io.gitlab.librewolf-community

[Desktop Action X]
Name=some name
Icon=different icon, should be used in app tray
Exec=/usr/bin/flatpak run --branch=stable --arch=x86_64 --command=librewolf --file-forwarding io.gitlab.librewolf-community -p PROFILENAME

[Desktop Action new-private-window]
Name=Private Window
Icon=view-private
Exec=/usr/bin/flatpak run --branch=stable --arch=x86_64 --command=librewolf --file-forwarding io.gitlab.librewolf-community --private-window @@u %u @@

[Desktop Action profilemanager]
Name=Profilemanager
Icon=configure
Exec=/usr/bin/flatpak run --branch=stable --arch=x86_64 --command=librewolf --file-forwarding io.gitlab.librewolf-community --ProfileManager @@u %u @@

So I have this entry with some actions. I want one action to launch a webapp. This could also be a separate .desktop entry.

Specifically I want to run Element Web, to avoid electron.

I use these resources to have a UI window without any of the Browser stuff, and it works fine.

But the icon used on Wayland is the generic one, and the app groups together with Librewolf.

Could I launch the process under a different name and use the WMClass to use a different icon?