As shown in the Graphene OS FAQ:
https://grapheneos.org/faq#clipboard

Quote:
"As of Android 10, only the configured default input method editor (your keyboard of choice) and the currently focused app can access the clipboard. Apps without focus cannot access the clipboard. This is a stricter restriction than preventing apps in the background from accessing it, since an app in the foreground or a foreground service cannot access it, only the foreground app that's currently focused. Clipboard managers need to be implemented by the keyboard chosen as the default by the user."

There is no message printing a similar warning when the clipboard feature is enabled (note that it is enabled by default).

I can confirm the behavior is as described above - the clipboard feature only works when the app is in focus (didn't try setting it as a default method).

The KDE Connect app can still write into the clipboard (e.g. sync clipboard to the phone when copying text in the laptop).