If we edit the Primary Skill field, then we receive the following error.
“You can’t assign a skill to a chat routed with Omni-Channel.: Skill ID”

Label of the field: Primary Skill

API Name of the field: SkillId 

Please check the following article. 

https://help.salesforce.com/s/articleView?id=sf.live_agent_transcript_fields.htm&type=5

Some fields might not be visible or editable. Primary Skill: Primary Skill is not used for chat and can be empty.