This is happening to me in Fedora 36 Silverblue, Gnome 42. I configured it to show up in the tray area (just like Bitwarden, for example). However, if I click the icon, I get the Gnome's settings user account window instead. Not only that. The icon only stays visible for around 10 seconds before vanishing. But, if I rigth-click the icon and click "Open 1Password" or "Open Quick Access" (before the icon dessapearing), both functions work and then the icon is gone again. Moreover, the icon stays in place if I keep the desktop app open. Once closed, the icon behaves as described. Hope this info is helpful.
1Password Version: 8.7.0
Extension Version: 2.3.2
OS Version: Linux Fedora 36 Silverblue