I tried changing many icons and files but nothing happened. The icons would always overlap after waking from blank screen. I think the bug is related to the appindicator extension.
And after finding out a little more I decided to delete gnome-screensaver and I replaced it with xscreensaver which FIXED my issue. I selected blank screen only and immediate monitor power off and it works great. And the icons don't overlap no matter how long I keep it in blank before waking it up.
Hope this forum helps someone in the future.
Here is the tutorial: Screensaver in Zorin 16
Thank you @StarTreker for your detailed help in that post!