Cool! Thank you for this information!
Yesterday I actually did some more digging and came across the KDE icon guidelines, as well, and they seem largely equivalent to the GNOME icon guidelines (more information below).
With regard to Cinnamon's different icon theme, both KDE and GNOME use the freedesktop Icon Theme Specification, which allows applications' default icons to be overridden at the system level:
https://specifications.freedesktop.org/icon-theme-spec/icon-theme-spec-latest.html
I don't know exactly what is necessary for implementing or enabling system icon theming for Joplin (if it doesn't just work by default), but it should be possible to modify your system icon theme to include an override specifically for Joplin. Additionally, you could request that it be added to the two default icon themes that come with Linux Mint, X and Y.
It's my impression that, while the install script does specifically replace the existing joplin.desktop file, this behavior could be modified and also would not be present if Joplin were distributed through apt, Snapcraft, or Flatpak.
EDIT: I just checked, and the version of Joplin I have installed on my Ubuntu is from Snap, and the update mechanism is maintained by a third party. (There is actually more than one third-party Snap, because reasons.) The Snap uses its own copy of the icon and it own version of joplin.desktop, presumably due to permissions issues. It would be nice if Joplin had official Snap and Flatpak distributions.
As I mentioned above, KDE's icon design guidelines are largely equivalent to GNOME's, with the main difference being that they strongly encourage otherwise flat icons to use a beveled bottom edge (which you can see in the calendar and terminal icons in my screenshot). They also encourage subtle gradients and foreground shadows, though the exact type of shadow is somewhat peculiar.
I could update the roundrect version of the icon to match the additional KDE recommendations, but in the case of the notebook version it's probably better without the foreground shadow.
Looking at the GNOME guidelines again, the sharp 45º shadow doesn't feature in any of them, so it may be preferable to do without it for the roundrect icon, too.