Along with various pieces of software, Flatpak also installs KDE and GNOME libraries needed to support them. However, it does not always remove obsolete versions of those libraries whenever software gets updated. One result is that messages regarding obsolete versions of GNOME may be issued and this has been known to cause confusion because there is the GNOME instance that is part of a Linux distro like Ubuntu and using Flatpak adds another one for its software packages to use. My use of Linux Mint may lesson the chances of misunderstanding.
Thankfully, executing a single command will remove any obsolete Flatpak libraries so the messages no longer appear and there then is no need to touch your actual Linux installation. This then is the command that sorted it for me:
flatpak uninstall --unused && sudo flatpak repair
The first part that removes any unused libraries is run as a normal user so there is no error in the above command. Administrative privileges are needed for the second section that does any repairs that are needed. It might be better if Flatpak did all this for you using the update command but that is not how the thing works. At least, there is a quick way to address this state of affairs and there might be some good reasons for having things work as they do.