Record triggered flow execution fails with the below error message, "Insufficient access rights on cross reference id" when logged in as a non-admin user

When a non-admin user attempts to create a Contact record in a Salesforce org where the User object's Sharing Settings are set to Private, the Record-Triggered Flow fails with the error: "Insufficient access rights on cross reference id."
The root cause is a permission issue at the database level. When the Contact record is created, the Record-Triggered Flow attempts to set the OwnerId on the record. Salesforce then performs a database access check to verify that the current user has permission to access the User record being assigned as the Owner. Because the User object's Sharing Settings are set to Private, users can only access their own User record — they do not have access to User records owned by others. This causes the access check to fail and the Flow execution to be rejected.