Make sure the user is not opening a duplicate tab or opening a record in a new tab. If they do, they will experience this issue.

Steps to Reproduce the issue:

1. Open Service Console app where Omni-Channel widget is added.
2. Set your status to “Available” or “Online”.
3. Duplicate the existing tab for the console app or navigate to another console/app within the same browser.

Result: Omni-Channel user will get Connection Error “Disconnected from Omni-Channel. Log in again to receive work.”

Reference Help Articles:
https://help.salesforce.com/articleView?id=000315768&type=1&mode=1

https://help.salesforce.com/articleView?id=000349123&language=en_US&mode=1&type=1