Yes and yes (unless you are using iOS). KDE Connect can sync the clipboard between any combination of desktop and mobile devices on Android, Linux, macOS, and Windows. The macOS version is still in development, but there is a compatible port called Soduto that works perfectly on macOS:
https://kdeconnect.kde.org/
The GNOME client is GSConnect: https://extensions.gnome.org/extension/1319/gsconnect/