“Assigned Work” tab is used to display the work items that are making their way through your queues.
Reference Article:
https://help.salesforce.com/s/articleView?id=sf.omnichannel_supervisor_work_tab.htm&type=5

If skills-based routing rules on a routing configuration is enabled, and assign the routing configuration to a queue, the queue’s membership no longer applies to the routing. The work will be routed based on Skills and not based on Queue Membership.
Reference Article:
https://help.salesforce.com/s/articleView?id=sf.omnichannel_skills_based_routing_comparison_to_queues.htm&type=5

So, if you are using Skill-Based routing, it won’t appear in “Assigned Work” tab. If you are using Omni-Flow and route via Skills, then also it won’t appear in “Assigned Work” tab.

Video Reference: