You could try it with KDE connect instead of Zorin connect. Few users had also problems with Zorin connect and they were solved by installing KDE connect. Please remove Zorin connect of your PC and smartphone before you install KDE connect (because it causes conflicts when they are installed at the same time). Then install it on your PC and on your smartphone.
"sudo apt remove gnome-shell-extension-zorin-connect"
"sudo apt install kdeconnect"
But it could be that it doesn't help. In this post a user wrote that Android inhibits clipboard:
Here is an exzerpt from userbase.kde.org about the clipboard plugin in kde connect:
"Clipboard -Share the clipboard between devices.
With this, you can simply copy text from your computer and it will be immediately available to paste on your phone, and vice-versa. This does not work with images though.
Auto-sync on Android 10+
Android 10 prevents apps from accessing the clipboard to prevent malicious apps from accessing your data. This makes the clipboard plugin in KDE Connect uncomfortable to use.
On Android 14, there's a tile in the pull-down menu called "Send clipboard", that can be moved to a convenient slot (e.g. in the partial pull-down section)."
Some clipboard managers only work in Xorg. You could try if switching to Xorg helps.