When a flatpak app is running in the background (e.g. as a tray icon once the main window is closed) on Wayland, a notification shows up asking if the user wants to keep it running in the background or not. You can test this with Telegram or KSnip, a notification shows up once you press the X close button and it goes to the tray. If the user disallows the app from running in the background, they can easily revert this setting using Flatseal (it's one of the last options at the bottom of the page), but they cannot with the Flatpak KCM. This is particularly problematic when combined with a separate but destructive issue where applications notify they're running in the background when they're actually not (this is the case with Firefox, for instance), so the notification appears when the window is still in the foreground. Once the user disallows Firefox from running in the background, the moment they try to open it, it closes again, making it impossible to use.
Up to now a workaround is to use Flatseal to change the "Background" setting.
*** Bug 470461 has been marked as a duplicate of this bug. ***
Can confirm, I use LibreWolf (which if forked from Firefox) and not knowing why it was asking me to close a background app that wasnt on the background I clicked to close. Then librewolf keep closing and was pretty hard to find this bug to solve the issue. Made a little worse by the fact that librewolf is my main browser, luckly I have brave as a spare browser, which asked the exact same question but I've clicked in "allow" this time. Can confirm this happened to me on both librewolf and brave even when the browsers where open and actually not in the background at all.
I believe the background app notification is being retired in Plasma 6. Will this issue become closed by then?
Yep, this is effectively "fixed" in Plasma 6 by removing the feature it would control.